Should be! Is there any growth remianing or did it snap off completly?

A better idea may be to salvage the bit that broke off, and see if you can root it, you may end up with many plants ;) rooting hormone would be best but can just work by letting the wound dry out a bit then put it in some soil ;) if you break it into many parts you could get a plant from each leaf segment.

I thought aloes don't grow from their leaves...?

Oh yeah, looks like they are very hard to propegate that way, but possible, as long as the wound is dried out and shrivvles shut before rot sets in its plausable, may need to aid it with that.
Tho may be too much effort ;)

Aloes do not grow from a single leaf but they will develop roots from the stem below a broken off rosette. Put it in a gritty mix and mist it , do not water it until the roots appear. It might take a couple of months. Depends on the type of aloe, where you are. once you see a root knub, then you can start to water. I have had aloes send out roots just lying on a table.

What kind of aloe is this?

Everything above the root level had been broken off/snapped off. The root system is completely intact, though and I let it dry out completely for a day, and it's now sitting in a small pot with some gritty soil.

I'm guessing it'll grow new rosettes soon right, or will the roots die?

The broken off rosette I just ended up throwing away because I didn't think it would regrow. Woops.

And the label on the pot wasn't too specific.

I'm almost positive it was this type

OH MAN that's a bummer. Nice aloe. The rosette would have been what you wanted to save first because it was of size already and just needed a few roots. Easy thing for it to regrow with all that stored energy in the leaves. Succulents are not like other plants. Come ask us before you toss next time. You mentioned rot above. Be very careful with your watering because the roots might already have rot.

Yes, you did the exact opposite from what's recommended, but if there's stem tissue in the root ball, it may yet grow an offset.

Oh, seems my dad actually saved part of the rosette. It has a big leaf and a few smaller leaves in the center, so I placed it in the small pot with the root system. Hope it grows!

The picture i posted isn't actually what it was; it was just what the aloe looked like by the way.

And there should be stem tissue above the root ball; It left a small nub of it so hopefully that'll grow too.

can you show a picture of the rosette and the stem portion to see if it is really stem or folded leaves.