If you need to repot it, it's as tough as old boots so go for it. Don't plant the trunk any deeper though as you'll cause collar rot and it'll die. Leave the soil level the same as it is now. The roots won't mind a trim. I had some in an old laundry tub and decided i needed the tub for something else. I just ripped the stuff out and dropped it round the base of a tree. Threw a wheelbarrow full of sandy soil around it and that was it. Knocked it around for about a month. Now its gone berko. I've never even watered the stuff.
I think the biggest problem with aloe is too much root moisture so normal potting mix should have some coarse river sand added for extra drainage.