That... is optimistic, to say the least. Languages evolve essentially by having successive generations pick up collectively on idiosyncratic features of the language. And of course, people who aren't talking with each other aren't going to pick up on others' idiosyncratic features, and after several generations, you end up with new, distinct languages. To keep a single language out of it, you have to work hard to promote only a single version of it, and rather literally beat the daylight of anyone who speaks the "wrong" version of the language (this is essentially how the modern "big" European languages came about.)
In other words, enforcing linguistic unity tends to require enforcing cultural unity as well.