That answer depends on how humans came into existence? In most fantasy worlds it isn't evolution, so for instance if a large group who all spoke the same language were transported from a different world into this one, then yeah they speak the same language and even as they spread out and grow they might still all speak the same language.Seriously, why the heck would there even be a single language that virtually all humans (and most others) speak? Common as used in D&D makes no sense at all.
Another thing to keep in mind is that in a typical D&D world there's a lot more world travel then is comparable to the real world history, and that travel helps to maintain a consistent language and limits the splitting off and isolation that leads to diverging dialects.