Interesting thought, and looking at how many Romance languages evolved from Latin in the past, there might be something to it. At the same time there are languages that managed to re-unite the different dialects, at least in education and literature, I am thinking about the Hochdeutsch for German [1]. So we have at least a counter example. Would be interesting to know what are the factors that lead for similar languages/dialects to become one or the opposite.
I kind of doubt that. The Internet, movies, TV, etc would keep us all connected enough that we would still all be able to understand each other. This article[1] even mentions some grammar forms where America and Britain diverged that have joined back together (I assume due to the Internet etc) ("can I", subjunctive, and British slang).
[1]: https://en.wikipedia.org/wiki/Hochdeutsch