See having watched all of campaign one, and a bit of the other campaigns where they are not struggling nearly so much with mechanics I would say the biggest barrier to entry for them in leveraging their brand to launch a new game is not any business concern but simply that they have all gained a hard won familiarity with 5e D&D, and won't really want to have to go through putting on a show playing an unfamiliar system again (and yes they do one-shots with unfamiliar systems all the time, but that's a different, "we're just doing are best" vibe than "this is our system that we created, are endorsing, or are the most prominent practitioners of" would be).
I wouldn't be surprised if they jumped ship rather than convert to 5.5 though.
I would be VERY surprised.
The show has a close relationship with D&D Beyond, they mention it most episodes.
Forgetting that, Critical Role, unlike others, clearly actually HAVE a special license with WoTC. Their published world is essentially official as is the adventure published for it. And their content has bled into OTHER official WoTC content (I know it bled into Avernus, for example).
Further, I suspect the great majority of their fans couldn't care less about the current OGL controversy (sure, there are some, but not the for the most part) so I doubt that's a factor.
Could it happen? Sure, But it will likely be MUCH later, if ever.