Can a GFI receptacle die coincidentally at the same time as wall drilling?
I agree that the question is a bit vague. I get the impression you're looking to either accept or absolve yourself of blame for the blowup with the HVAC company. My thoughts: 

Sure, coincidences happen. You don't need us to tell you that. GFCI receptacles can last from zero to many days. 

It's unlikely that the receptacle was damaged remotely without a heavy load on it, such as a refrigerator. Either a cable was shorted, and that resulted in damaging current through it to some load, or the receptacle itself was damaged. You'd know if the latter was the case, and without forensic analysis you can't know about the former. Of course, it's possible that there are factors you and I don't know about.

Finally, it's odd that you as a tenant got so involved. In the future, let your landowner handle it. Go get a pizza. :)