Probably less prone, likely much less. There is virtually nothing on the bottom other than the main battery. Potholes and debris are just as hard on a Tesla as any other car (it is really heavy) and demands precise wheel alignment. But the underside of a Tesla is basically a sealed compartment, and there is very little plumbing to tear up.
Much less. In fact the adjustable air suspension is one of the reasons I got the MX. If you have a rough patch you can raise the suspension--It will keep track of there the rough spots are and raise and lower automatically according to your input. BUT you want the more robust 20” wheels/tires for sure.
I haven't met a lot of other Model X drivers who take their car regularly on gravel roads, but there are some of us out there. I'm using my an Audi (Q5) and several Subaru's (Impreza, Forester, Legacy) and as a measuring stick here. The undercarriage is actually better protected than an ICE vehicle. One area that does seem to get a lot of debris pickup is actually the brakes. Rocks seem to get stuck between the calipers quite often for some reason and cause some squealing. Pumping the brakes usually gets them to loosen up and fix it.
The other area is the black matte wheel well trim. That seems to be the first to break if you really push the limits of your car - which would be beyond just potholes, dirt/gravel roads, etc. On a one lane, two direction gravel road both cars will often pull up on a berm to get past. Most of the time it was fine, but I did pop that trim out a couple of times. It gets cracked, but just pops right back in and looks normal again.