Ive used a Makita 9 1/4" saw to cut up concrete slabs in the past: 3 1/2" approx depth of cut in a 4" slab. Gets a bit slow when severing steel reo rods, but otherwise OK. A Festool is as robust a saw as any other, so there's realistically no valid reasons why it can't be used similarly.
Just remember that it's going to be hard work on the saw. Hard material plus full DOC all the time, so be careful to maintain max revs for correct motor cooling; i.e. don't force the saw, & don't let it get too hot.
I've also used a guide rail mounted smaller saw (Metabo KSE 55 Vario Plus) to cut fibre cement 3/4" & old marble wash stand tops & thicker pink granite hearthstones (1 1/4" ??) successfully. In this case, with a smaller blade. I think it was a 125mm (5") fitted to the 160mm saw. Fitted to the guide rail, progress was pretty slow due to the reduced blade rim speed.
It also tended to gunk up the saw's plunge & scabbard retraction mechanisms, which required extensive cleaning after: air blast & a toothbrush & relube. Standard dust extraction occurred fairly satisfactorily, although I also flushed out any dust &/or slurry residues from the hose whilst still fresh & damp. Leave it to dry & you might have problems.
Fiber cement was cut dry, the concrete & stones were cut with just the tiniest trickle of hose water for lube & cooling purposes. An inline RCD was added to the power supply, on an already ELCB protected circuit. Sort of belt & braces.
The only other (rather obvious) suggestion is, as with any other sawing operation, to mount the blade the correct way around. Even continuous rim diamond blades (that will provide your smoothest cuts) have a particular cutting direction. Sorry if I'm insulting your intelligence here, but I've made this mistake myself.
Continuous rim blades will actually be faster, as they bring more diamond grit particles to bear than segmented blades have. They're also much less likely to chip the substrate surface. You still won't get a lot of life from your blades working such hard materials: if possible choose "hard" material grade blades rather than "abrasive" grades.