Actually, based on how I understand the way GFCIs work, I was concerned about the opposite case - leakage out the chassis ground that was not problematic, but WOULD cause the GFCI to trip.
As I understand it (based on web research, for instance:
here), a GFCI basically sums up all the current through (in the case of a double pole breaker) both hot lines and the neutral, and that should sum to zero. If any current is going through the ground (which should not happen under normal circumstances), then the sum will be non-zero and it will trip the breaker because of a ground fault. If the HF chassis ground ever carries enough current at a frequency that the GFCI breaker is sensitive to, I could see it potentially causing a problem.
But Rambozo is right - the proof is in the pudding. Whenever I eventually get the PP256 I'm lusting over, I'll try it out and let you know. In the meantime, I think I will swap out my 50A breaker for a GFCI breaker, because the outlet is in my garage and therefore technically should be GFCI protected. I hope it doesn't cause problems in the future, though, because 2-pole GFCI breakers ain't cheap.