No it won't, obviously if it copies code exactly then you can't use that. The question is whether Microsoft is liable for the fact that Copilot has the ability to output copyrighted code sometimes or whether people using it just need to check that it hasn't done that before using the code (Copilot can also do this automatically)

Google can also show you GPL code in its results, but people aren't trying to sue Google and the user is responsible for checking the license before using it (though Copilot makes this harder)

Disclaimer: I haven't read much about the actual lawsuit and I'm not a lawyer but I assume this would be the case