it seems there's no neurolinguistic limit on how many letters can a language's alphabet have (it varies a lot between languages), the IPA is a huge phonetic alphabet, As of the most recent change in 2005, there are 107 letters, 52 diacritics and four prosodic marks in the IPA.
We simply do not know: this is an empirical question, and nobody has done the study. The problem with writing in IPA is that you have to understand what the various letters "mean". It's easy for Saami speakers to learn that the letter č "means" (in IPA) the phoneme /tʃʰ/ and ž "means" the phoneme /tʃ/, and the don't need to worry about low-level details. In earlier practice, you had to attend to more phonetic details as opposed to the phonemic system, and it was harder to read. The problem with teaching IPA is that subjects do not have a solid reference framework: you can't get the average person to solidly learn what "ɬ" means, and many linguists don't really have a reference framework for "ɤ,ɜ".
If the goal is to enable a person to at least recognize most variant transcriptions of words, you will need to train them on the myriad consonant and vowel qualities encountered in the language. For example, they would need to know that English [flæ] is spelled "flour" and [flaʊə] is spelled "flower" (depending on dialect), and they would need to know that [ɺeoba:d] and [lɛpɹ̩d] are the same same word in different dialects (when presented orally, American English speakers do not recognize the first pronunciation).
A narrow transcription involves lots of "adjustment" letters, possibly indicating that the phoneme /e/ in some context is a bit higher and further forward in some context, so you'd have to train the subject on the distinction between [ɪ] and [e̝̟] which if you can't see it involves the advanced and raised diacritics. The most efficient way to do this is to tell people to ignore all of the flyspeck, and teach them some simple rules like "ɾ is t or d, you just have to guess", "ɺ is either r or l", "turn [ħ] into [h], [ɓ] into [b]...". The problem is that you could not get willing but "statistically valid" experimental subjects to put up with this. You could perhaps perform the experiment on a set of graduate students in phonetics, which would tell you about graduate students in phonetics, but not people in general.
Any studies of reading fluency (e.g., can people read fraktur better than antiqua?) boil down to the trivial: One reads best what one is used to read.
It is also known that we skip a lot of information encoded in the writing, e.g., we don't notice a lot of typos or printing errors because the redundancy in the written language is that large.
So, given a standardised phonetic transcription and enough reading practice, I see no reason why one shouldn't be as fluent as in orthography.