No it doesn't. The problem with the sonic boom in fighter jets and the associated forces it produces is because the control surfaces of the planes at the time weren't designed to deal with the effects from supersonic speeds[0], so they would lose control.

There is no 'force' associated with breaking the sound barrier, as most would imagine

Most of the forces in the freefall would have been G forces from the tumbling or spinning motion as he jumped out.

[0] the tl;dr for aircraft is that as you approach and overtake mach 1, at some point the airflow at the beginning of the wing is supersonic while at the rear of the wing it is not, as you accelerate this point moves from the front of the wing to the rear. the problem is that it causes the airflow from that point to separate from the wing which results in a stall, spin, crash etc.