I don't think so; from a quick glance, I believe the theorem deals with inconsistencies when dealing with infinities, and the program and its output are all finite. If the program hangs or runs out of disk space, then that might be confirming evidence for the theorem ;-).

No,

An consistent theorem system can know no bounds. There's halfway. If Peano arithmetic is inconsistent every statement in it is provably true and false. QED.

It doesn't matter if the program is unreliable, since it generates proofs that are easy (but tedious) for a human to check.