So, I can tell you that I have a GFCI outlet in my house that randomly trips. I installed a GFCI outlet when I first setup a tank and it ended up tripping when I was out of town, wiped out most of my fish. I have since upgraded aquariums and moved to a different location in the house with a new GFCI outlet. I let the old one in place and it randomly trips with nothing plugged into it, and as far as I know the only other thing on the circuit is the light and ceiling fan in the living and a couple other outlets that also have nothing plugged into it. I'll come home maybe once a month to the living room light not working due to the GFCI tripping. Maybe the light has a problem... or maybe its just a really crappy GFCI outlet.....
That being said, I have taken measures to make sure that an accidental trip doesn't crash my tank again. I have one powerhead on a battery backup in the main tank, and in my basement I have an airpump that is on a UPS that will run if I lose power down there.
I have had equipment that has gone bad over the years that has tripped the GFCI. I've had a few pumps that started tripping GFCI and they immediately got tossed in the trash.
Having said all of that... I believe that GFCI is important, but be prepared if it does trip.