Perhaps not, but your mobile carrier will! I use a Pixel 5 with LineageOS installed (and no google services), but I also needed to install Google Docs for a project (since the web interface refuses to load on Android) which means that Google is still able to access my IP address–but I think that’s better than Google’s “location history”, or Play Protect on Android sending a list of all installed apps
I generally like being as close to mainline/AOSP as possible, and I used LineageOS for years on my Essential PH-1. That being said, it does look like the Pixel suffers from no lack of custom ROMs, so I may “distro hop” for a bit in the future