The PS1 doesn't an FPU but got a version of Quake 2, so it's possible. That said, it was somewhat different from the PC version, so it could be argued that it's not the same game.
The PS1 version definitely has its own engine, which is not just a port of the Quake 2 engine to the Playstation, but a new engine.
The PS1 version definitely has its own engine, which is not just a port of the Quake 2 engine to the Playstation, but a new engine.