You have a good chance. I was RWT banned a couple of years ago.
I just told them that I was not RWT, but rather I was quitting the game and giving things out to long time friends, both in real life and in game. Just tell them that you were too poor in real life at the time to buy things, and really too generous to want to sell things.
"Good afternoon Jagex team, I am currently appealing a RWT ban I received four years ago and hoping to make light on the situation. I'd like to start by saying that I was not real world trading: I was too poor at the time to ever buy gold, and didn't really care enough to sell it (why risk the ban?). I was, however, quitting runescape while I went off to college and gave a few friends of mine some items while I was leaving. I'm sorry if you took it that way, but I assure you with every part of me it was not. I'd love to play RuneScape again, and hope we can resolve this."