3D FPS are being created since nearly 30 years, now... computers have seen their speed multiplied by... huh... several orders of magnitude. Same for network controllers and infrastructure.
It would be shame if godot was not fast enough.
Now, the question is probably, how much is it worth using it compared to other solutions, and for that, I'm afraid I don't have precise answer.
To answer, someone would have to start by defining the type of FPS. For example, in unvanquished, the difference between a head, a torso and legs is just about how high you hit the BBox. This is good enough for arena shooters, but it might not be in stealth games (pace difference).
Then there is how you intend to configure the bots, if you want bots, of course. And how the network is handled: do you work with TCP, with UDP, with something in-between? Do you do P2P or centralized calculations of the actual collisions?
And when you know the answers to those, "just" check what godot can, or can't, do in that regard.
Of course, there is probably other concerns to think about...