In The Light in the Piazza, there were some songs/dialogue that you could get the gist of what they were saying through context, expression, gestures, etc. It also helped to immerse you in the same situation the Johnsons found themselves in, trying to communicate in a foreign country, not quite understanding either.
More importantly, it illustrated how a difference in languages could easily mask Clara's "condition", making it seem an opportune situation for the mother to drop Clara into...a place where she might have a shot at happiness/love where they mightn't realize there was something wrong with her.
For this show, it had a specific purpose that, I think, worked. I saw the show a few times with people who are not sophisticated theatre goers. Not a one of them had a problem with it and all understood its place in the show.
So I guess, to answer your question, audiences will tolerate as much as works and makes sense in a particular show.
Art has a double face, of expression and illusion.