Google pay won’t work, but everything else should. I’ve never experienced any of the issues the other commenter had, and I’ve installed Graphene on 4 devices (not dismissing you BTW, just saying I think your experience is quite uncommon).
I don’t think third-party launchers are a good idea (you’re giving full device permission to an unneeded app) but it should work.
Almost every app I wanted to use worked with Graphene before they introduced their sandboxed google services, and now everything I’ve tested works with Google push notifications. The only exception is Google pay, and there are upstream reasons for that. Keep in mind, on a very rare occasion the hardened memory allocator breaks compatibility (again this is very rare), but there is an app-specific setting toggle to turn this off so it’s kind of a non-issue.