I don't think we have enough information yet.Assuming Joe K's data to be correct ... I am not sure exceeding the speed of sound is impossible by a falling person...
The two drag factors are air resistance and shock wave.
Without either of those, any body, of any mass, would accelerate to a value beyond the speed of sound after falling for about 6km (around 3.75 miles).
In the earth's atmosphere, even at rarified heights, air resistance at the speed of sound would have a heating effect. I don't know how to work out what the temperature could reach, but clearly it's an objective that the speed of the skydiver doesn't cause him to be incinerated.
Regarding the shock wave(s) that present the 'sound barrier', I don't know whether or not these waves depend on the presence of an atmosphere in order to exist at all. Since the simplistic, but correct, view is that sound cannot travel in a vacuum, then I'm inclined to expect that the intensity of any shock wave, and therefore the drag it presents, is proportional to the density of the atmosphere. Therefore, I'm inclined to expect that 'breaking the barrier' is easier the further away from the earth that the skydiver starts his descent.
Another practical consideration is the means of deceleration. I don't know much about parachutes, but attempting to open and function at the speed of sound seems a lot to ask of one. The ground would decelerate him exceedingly successfully, but he would be unlikely to live long enough to enjoy the celebrity ensuing his silent 'sonic boom'.
