Depends on the betta, no sure way of saying unfortunately. I've seen a betta nip of the antenna of apple snails.
I wouldn't recommend an apple snail for a 2 gal either though. You would need a decent filter (likely bigger than the one the tank came with) to get away with it, and a tight fitting hood (as in a tank as small as 2gals, the snail would try to escape).
Also remember, most decent sized animals you can add to 'clean' the tank will only add to the waste anyway (this certainly applies for apple snails) as you have to feed them food, and this is inevitable just turned into poo that sits at the bottom of the tank.
Apple snails wont survive off waste food in the tank alone.
If you set up the tank right with plants and a proper light, you could have cherry shrimp, but again, some bettas just don't like these.
Regardless, you are going to have to wait a while before you add anything, as the tank is only 2 days old.