You know, what it all comes down to is this - if the only reason you're playing an RPG is to screw with the GM, no matter how good your intentions for doing so, you fall under a number of terms that I am not allowed to repeat under this word filter.
There are too many issues available in an RPG where time travel becomes a "thing" for them to ever properly be solved. The only thing bigger than a regular plot hole is one that tears into the space-time continuum. So claiming you're doing it because you can patch issues in RPGs that follow that one... no.
If you're playing an RPG with the intent of damaging it, than you're too immature to be playing on a forum mostly used by teens through young adults, and should go back to kicking down other peoples sand castles in the kindergarten sand pit. Obviously, that should go without saying, and I understand most people here are just joking around. Still, somebody reading might actually take the concept seriously.
The only exception to the above is a railroaded RPG. If you're being railroaded, look for every opprotunity to get off.
Now, obviously, what is always the most important are the characters and story. If some strange loophole or exploit will provide advancements in terms of actual character development (not just a power upgrade) move for it. Talking to the GM might be your best option for that, though.
That being said...
Exploitation, loopholes, and so forth is not the biggest problem plaguing a time travel RPG. The biggest problem is that an RPG with that much expanse of time requires a much larger player base than one with only one time frame, and that kind of player base is virtually nonexistent in the present time.
-Toa Levacius Zehvor
"I disapprove of what you have to say, but I will defend to the death your right to say it."
- Evelyn Beatrice Hall (often attributed to Voltaire)