I think this depends entirely on what era you're looking at.

So far as I am aware, there wasn't an institution in Rome that said "Ok, everyone, amicus is a second declension noun, not a fourth declension one!" I'm not sure how linguists would approach this issue, so I can't speak to how everyone agreed that it should be "amicus, amici." There doesn't seem to be the same variation of dialects that you get with ancient Greek writings.

However, the educational curriculum was extremely conservative insofar as people studied the same Latin texts regardless of where they were in the empire. By the late antique period, people studied Vergil and Cicero (and a few others), and being able to write like them was considered the gold standard of Latin writing.