I am native Armenian speaker. I know Russian from childhood. Recent years English became my second language and I am using it in everywhere except interaction with friends. Now I want to learn Italian. Do I need to learn Esperanto first in order to make my job easy and more consciously.
There are much more propedeutic languages. Latin is the first that comes to mind but if you already knew it. Learning it on purpose for Italian is not really convenient, you'd be better off using that time to learn Italian directly. If you had knowledge of Spanish and French, that'd be certainly a good help.
Spanish is very similar to Italian (a stereotype says that you just need to add an S to Italian words to get Spanish, which is of course wrong but gives you an idea of their closeness). Many words are basically the same (the words for yes and no are the same except the graphic stress which is the opposite: sì/sí, no/no).
French differs a bit in terms of some grammatical structures and vocabulary but it's close to Italian as well. If you had prior knowledge of these three languages, then you'd be at an advantage in learning Italian, but if you don't know them, just go ahead and learn Italian directly: if you choose to learn those later you'd have Italian as a prior knowledge.
Concerning Esperanto: I agree with the others saying that I doubt it'd really help you. I haven't never studied it but I have seen some material written and I can say it didn't feel really "italian" to me and I'm a native italian speaker. If you don't have to learn it for personal interest or other needs, feel free to skip it and go straight to Italian. :)
I would say probably not. Despite its name, Esperanto is not a simplified Romance language. Though much of its vocabulary comes from Romance languages, its phonemic inventory is Slavic, and its morphology is agglutinative. See the Wikipedia article on Esperanto for more details. https://en.wikipedia.org/wiki/Esperanto#Linguistic_properties
As far as I know, the grammar of Esperanto, though it is simple, is so regular and embodies so much invention that I'm not sure that it resembles Italian grammar enough to serve as a stepping stone to learning Italian.
I am not a linguist, and only speak one language, my native English, so take my answer with a grain of salt.
The study in the TED talk you referenced was for students who probably had not learned another language before learning French.
The reason why Esperanto was considered helpful was because it allowed the students to become acquainted and become comfortable with speaking a language other than their own. Esperanto is very simple and shares roots with many languages, building the confidence required.
In your case, you are completely comfortable with multiple languages (Armenian, Russian and English) so the benefit of learning Esperanto to learning further languages will be minimal.
I would not say, "go for it before learning Italian, Spanish, Portugese, French or Romanian..."
However, if you're tempted... it will expose your mind to a linguist life's work.
I think Esperanto helps understanding/accepting/explaining different language structure mentally. Easily.
Nonetheless, be aware that Esperanto have lots of roots from all european languages: Spanish, French, Italian, English, German, Latin, Russian, Slavic...
This is only my personal experience: I learnt esperanto in... 2005. I never mastered it. At most I knew 200 words. At most because I was learning reading the book: "Esperanto per iom pli ol 200 vortoj" by Aleksandr Kerbel. (I think there is not a single foreign word in it. Only drawings and esperanto. Well that's the way I remember it...)
But Esperanto grammar and vocabulary is so concise, regular, and modular, that I was able to read the "Persian Letters" by Montesquieu in Esperanto, with simply the help of a little dictionnary before even finishing my 200-words learning book.
It is a really refreshing feeling when you grasp its expressiveness.
There have been studies (or at least small amounts of research) done on Swedish University students, among other nationalities, where the students learnt Esperanto AFTER already knowing multiple languages (in the case of Swedes, most know English, Swedish, and French/German/Spanish at least - and then continue their third language or pick up a fourth one in Uni). There was still a significant improvement in the people who learnt Esperanto compared to the normal people. Sadly I can't link you to the info on this where I read it, as it's in Faroese which doesn't even have Google Translate.
The basic idea is, if you're already very strong in grammar then there's no need to learn Esperanto. If so, the only way it would help, would be in vocabulary, as Esperanto's vocabulary is something like 60% Latin or Romance. This actually isn't something to scoff at, as there have been a few studies where ex. people who knew Esperanto could translate a French sentence without having ever learnt French (I personally, just today, understood a basic Spanish conversation that I was overhearing, thanks to Esperanto too). If you're a bit weak in grammar, for example you always forget when to use an adverb, then Esperanto will still help. And in all honesty, it's so fast to learn that it can't hurt you to spend some time on it even if you think it's useless - at the very least, you can easily find an Italian penpal who knows Esperanto well enough that you two can actually talk properly enough for them to give you really good help on Italian (this is relatively hard to do in English).
@TIKSN, please be patient and read the following:
By definition we are always biased when we judge an experience unsuccessful or unuseful when we do not give everything we can to make it successful or useful. You will always find what you are looking for.
The primary goal of Esperanto as an auxiliary language is to "facilitate the communication" so people can rapidly and easily communicate and learn about each other cultures. Hence its nature as "auxiliary".
Esperanto is a highly agglutinative language, because it uses a word-building mechanisms to rapidly build new words from roots.
In the same time, its regular grammatical structure allows learners to easily develop a feel for nouns, verbs and adjectives. A straight forward simplified pronunciation: One grapheme (smallest writing unit) corresponds to one phoneme(unit of sound). As a result it allows learners to become quite proficient with a minimum amount of effort and time.
Knowing that, there is more than 6000 languages in the word, to not overlook anyone of them: national, regional, tribal... and each one is tied to a country, region, culture, history... Why should one or few national languages be better than others? Isn't that language discrimination?
Esperanto doesn't belong to any country, and everyone can adopt it. Because it has indo-European roots and highly agglutinative characteristics, it offers a very quick and easy solution to communicate between people of different cultures and languages without any military, colonial or economic hegemony. It helps preserving the diversity of languages which is as important as the diversity of species.
I am not blaming main languages themselves, but the way they aquired their "International legitimacy". This is not the case with Esperanto, it is only a vector of communication intended to be a springboard to other languages and their cultures. With esperanto we immediately start efficiently communicating each using his/her own culture. The culture of Esperanto is what we obtain as the result of intercultural communication.
When Learning a language and live it day by day it is like discovering a parallel world with its reality and its people.
I regularly participate in local, regional and international meetings, congresses... and I can find people speaking Esperanto in every country I visits I have friends ALL over the world with whom I speak only esperanto. I have build many projects, professionally with esperanto collegues and my friend childrens have Esperanto as their native language.
Comparing to other languages, it is very young but mature enough to be efficiently used for international communication.
For sure, it is going to be tough to go against the historical determinism of the main languages, but it is worth it.
Take a look at these websites for more inf.
Here is a recently appeared book about the subject, might interest you.
Esperanto as a starter language for child second-language learners in the primary school,
Karen Roehr-Brackin, Angela Tellier, Lingvistiko, Esperanto UK, 2013 (2a eld.).
Resumoj de la malkovroj faritaj kadre de la projektoj "Springboard to Languages". Prezo: 12.30 EUR. Pliaj informoj, reta mendilo: http://katalogo.uea.org?inf=9012