That is an excellent question and I wouldn't put it past them. Only time will tell.
They are already throwing a fit because Chinese companies are distilling their models, so them trying to copyright their copyright infringement machines is definitely plausible. And with a US system as it exists today, it might very well work. Hopefully the rest of the world will have told the US to fuck off by then...
Microslop is one step ahead and has an online editor with Copilot integrated into it. That makes the chance of getting an LLM assisted or written PR even higher. Knowing Microslop, hey will go even further and have Copilot activated on all active repos, submitting PRs - and CoPilot will be opt-out
I wouldn't put it past them.