There could be a small element where a wider cultural diversity, in that kind of situation, yields a wider variety in products, goods, services, etc., but that is very much contingent on those cultures actually promoting good, useful, positive habits and interactions.

I'm reasonably certain that hypothetical positive results of that sort though are pretty uncommon, even in the wide range of historical examples one can look at. Especially when said immigrants are imported because they have nowhere else to go (refugees) or because of political plays, particularly since either of these kinds of instances tend to import them in larger numbers than could offer any benefit.