I'll answer only from my personal experience: As a Brazilian, and so a Portuguese speaker, I know it's very common when tourists from Argentina and Uruguay come here, or when we go to these and other neighboring countries, that we both speak our own languages and, although we don't always know how to speak the interlocutor's language, we pretty much understand them and they pretty much understand us.
Well, today I speak a considerable amount of Spanish, picked up in the time since my first contact with them when I was 10 years old and we moved to the state where I live and I met a lot of Argentinians on the beach. It's pretty natural.
Sometimes things don't work perfectly, and there are some words we must be careful with (e.g. innocent Portuguese words that are similar to dirty Spanish ones), sometimes one person must repeat what was said or say it again in another way, explain, etc. But it's usually possible to communicate without having to learn the other's language. Sometimes I understand a Spanish speaker better than I understand Portuguese speakers from other regions of Brazil, actually.
So, coming back to your question's focus, I know I used as an example two closely related Romance languages, that are easily understandable to each other, and I also know that it wouldn't work, for instance, between English and Portuguese, German and Spanish, or Chinese and French. But maybe, if we all could learn one "sample language" from each family, plus develop some non-verbal abilities (as communication isn't just verbal), it looks like something reasonably possible.