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.
This is slightly misleading. There is wave drag, which is caused by the formation of shocks. This happens when the plane/body is nearing the speed of the pressure wave it creates ahead of itself. The air no longer has sufficient time to flow around the body in a smooth (or even turbulent) way. Instead it piles up into sharp discontinuities called shocks, with very low pressure regions behind the shocks. This produces a lot of drag, several times more than that due to viscous drag alone. That's where the concept of a 'sound barrier' came from. People weren't sure what the maximum drag would be, or if we could build engines powerful enough to overcome it. Obviously we can and did.
But in the case of free fall from space or near space, the air is so thin that these effects are minimal. Also his starting velocity moving through the thin air is much lower than say a reentering space craft, so the whole thing is much more mild and manageable. By the time the air gets thick enough to worry about, he'll have shed enough speed to even the slight early drag to be at a reasonable terminal velocity. (This is the same concept used by SpaceShipOne's 'shuttlecock' re-entry).
A. Starting height = 39045 m
B. Desired speed = 343 m/s
C. Acceleration = 9.8 m/s/s
D. Average speed while accelerating = 171 m/s (half of B)
E. Time to reach desired speed = 35 s (B divided by C)
F. Therefore distance travelled = 5985 m (D times E)
G. Therefore altitude at Mach 1 = 33060 m, give or take the small amount of drag.
Edit: Meh, I see from the video that he didn't accelerate as fast as this, I guess the drag was significant after all. Even a small amount of gas will move you if it's coming at you at significant speeds...
He was just asked this at the press conference, and he replied that he felt nothing as he is in a pressurised suit (he could neither feel or hear anything during the fall).
