Yes, it's possible but as long as you make The M.O.T tester aware that your car has an LSD there shouldn't be any problem. A diligent tester will bring up on his computer any special requirements for the car he is testing anyway. Now then, my mate owned and ran an M.O.T garage for over 30 years and he told me that he only used the Tapley for vehicles with permanently engaged 4wd. For cars with LSD's he simply ran the test with both rollers running. He said that using a Tapley for a road test is pretty worthless as this only gives you an overall braking efficiency test on all 4 wheels whereas running on a rolling road (with both rollers running) gives the tester a lot more information on the rear brakes .
Pete