you’ll definitely be loosing security, which can turn into loosing privacy if you get affected by malware.
you’ll also be loosing privacy if installing proprietary apps, since GrapheneOS has features like storage scopes and a better permission system that help minimizing privacy issues.
I think that locking your bootloader in a Pixel is possible regardless of the ROM you install.
Anyway, I think that there’s no real benefit of installing any other custom ROM in a Pixel other than GrapheneOS. You’ll be just loosing out in security and potentially privacy for no real reason.