Doubtful. Without Linux running the majority of the internet, I doubt the desktop scene would look the same as it does today.

I’m not an expert, but any time I’ve needed to do this, I set up my own router as a client to the parent router, and I set my router (client) as the DMZ in the parent router. Effectively you end up with two routers that are both (more or less) connected directly to the internet, without the two networks messing with each other. It’s also minimally invasive to the parent router (even old stock firmware has always had a DMZ option).

The tricky part then is using the wireless connection as your “WAN port,” rather than a physical one. In which case, as long as you can install OpenWRT on it, you should be fine.