I tried this before on an XBox controller by mapping Left and Right brakes to LS+LT/RT respectively. Mashing the stick down and pulling both triggers for dual braking, easing off a trigger for differential braking. The rudder, of course, did not engage when the stick was depressed as the only command being read were the brakes.
The problem was some strange rudder/nosewheel effects if you released the stick before letting off the triggers, as the rudder would suddenly come into play. The rudder/nosewheel would ‘stick’ at full deflection until you hit the thumbstick again. I guess one could work around this using LS+LB/RB instead of the triggers.