My mother gave me an aloe vera plant that she had taken from a larger plant. Because it hadn't had enough room, it was growing sideways and downward. I have propped it up the best I can by sticking a fork in the pot and tying a strip of fabric around it. I also have it leaning up against a window because the fork wasn't strong enough. My question is, will having something constantly touching (the window) hurt it?

It can yes. leaning any plant right on a window can possibly cause the leaves to get cold damage or burn later on.

If it's without roots, maybe cut the stem back mores so it can sit down more inside it's pot, eliminating most of the lean, or, set the pot it's in now down further inside another larger pot so that at least half of the aloe leans on the inside walls of the bigger pot until it hopefully straightens out down the road.