I think you could plant it deeper, but not several inches. Maybe an inch deeper. Whatever you decide, let any raw broken or cut ends callus over before you plant it deeper. If you put the raw ends into the soil while they're still "wet", it will invite rot.
If you have some broken leaves, you can let the ends callus and then plant them in soil, too. Not all aloe species will start a new plant from a leaf, but some will, so it can't hurt to try.