Possibly, but I think if YC companies could get away with just cutting everyone they would too.
I don't doubt there's an impact here, but it's not because they have a real interest in any other topics that concern me and hiring, H1B and so on.
All companies would prefer to have 0 employees if possible. This isn't special about YC companies. Heck it's not even special about companies. If I could buy a roof that was slightly more expensive but I never had to hire a roofer I would.