The saturation switch adds zener clipping diodes at the end of the preamp. Mesa Mark stuff certainly doesn’t have that on the real amps (unmodded, ofc). I’m not sure about Friedman amps but I don’t think they do either, but if I’m wrong then happy to be corrected.
I don’t know exactly what the fat switch does to the circuit, but again I don’t believe Mesa stuff has that on the physical amp. Perhaps the Pull Deep things on the Mark series are the same thing, but there’s a separate model with that engaged, and on the Triaxis it’s engaged by default IIRC, so turning the fat on as well would basically double up on the same thing.
Saying the fat switch ‘doesn’t apply’ makes me think you’ve read those posts about the Mark series needing the fat switch engaged to sound good, but it’s really a matter of taste. If you like it with the fat switch on, do that, if not then just leave it in the ideal tab.