yikes.
when you say your reef rock will die, do you mean bacteria from cycling or do you have actual livestock. Either way, its not worth the risk, but if you have livestock, you might need to take some steps to keep it going. If you are just worried about the cycle, I would not. It will cycle again just fine. And it will cycle a little many times over its life. So don't take risks just to avoid re-cycling.
I think many extension cord GFCI's trip are more likely than wall-mounted units to false trip. I don't know why I think that. I've had plenty of both. But you need to know if your outlet is grounded - a plug in style won't work any more than an outlet style if there is no ground.
I'm glad you brought this up as an emergency, but my suggestion is to take a step back, and accept that it may take a few days or even a little bit longer to resolve this, and then worry about your cycle.