To the extent that OBS can use an eGPU on MacOS, if you are running OBS on a display connected to your eGPU, you are using it.
The OBS log will indicate near the top which GPU it is running on if you have more than one installed.
W/r/t use with FCPX, do you mean rendering or encoding?
Rendering in OBS does not use CPU, only GPU. Encoding uses CPU. An eGPU can't be used for encoding unless it's made available to OBS through the Apple VT Hardware Encoder. So if you have that available to you and it works, then yes. But having an eGPU doesn't give MacOS access to encoders it doesn't have software for (like NVENC).