Hello,
I know the question is pretty much answered
but due to the rather "importance" of safety here, I want to comment:
1) Personal safety is paramount, much higher than the cost of the inhabitants
2) Just like Tony said. GFCI "will" not trip. If it does, well better let it trip and find out what's going on. Definitely take the whole thing apart if that's what it needs to be done to find out the root cause of it.
3) GFCI is one of the first five items that I installed when I started in this hobby.
4) I have been away from my tank for a maximum time frame of 2 months for at least two times, in addition to multiple aways each of a full week time frame. My GFCI never tripped. And this is the case because there were no hazards and electrical issues with the setup.
So conclusion (on my part at least) is to go ahead and install it.
Titus