They have already done this with Chromium Embedded Framework (CEF) which I use in my everyday browser. Since it can't do logins, even things like Google Groups fails auth and I'm forced to use Chrome instead of Chromium.
It is very annoying, Google announced it well ahead of time, but in general just doesn't care. They suggest the browser integrate with external auth options as if I want to customize my browser for Google auth.
They're actively fighting certain user agents with secret heuristics after having people create/need Google accounts for lots of things. Bastards.