Just curious, would having hot and neutral reversed on a GFCI receptacle affect its operation? Reason for asking is I had one that would sometimes trip and would not reset. Corrected wiring and now seems OK. It still may be bad but the fact that it was miswired got me thinking.
My Opinion: Your question is a lot more complicated than you would think. There have been so many different types of GFCI protected receptacles manufactured over the years that it would be impossible to say what they would do.
I went to a house one time where a home inspector had written up all the GFCI protected receptacles not tripping when he used his plug in tester.I used the test button and they tripped and then I used my plug in tester and they worked so I started to wonder what was going on. I called the guy and he and I had a talk about this to see if we could figure it out. It turned out that I was using an Ideal tester and they tripped and he was using a Sperry tester and they wouldn't trip. I even went to they local HD and bought a new Sperry tester and it would not cause the receptacles to trip.
I'm pretty sure that the difference was a different resistance to ground used by the different testers. I suggested he buy a different tester or to rely on the test button.
Back to the original question: I have actually seen GFCI receptacles that had revered line and load that would work but naturally the test button wouldn't function properly and there was no feed through to down steam receptacles.
When I have any kind of a problem with a GFCI receptacle I just replace it with a new one of good quality ( at least a good brand name).
Edit: When installing even a new GFCI receptacle use the test button a couple of times because I have seen a couple that were not working properly right out of the box.