Unfortunately, and rather unusually for the game, the answer is no.

With Gorgeous Grampa, you got the costume whether or not you had Grampa Simpson. It stayed in your inventory until you unlocked Grampa Simpson – and I’d assumed that Fruit-Bat-Man worked in the same way. However, probably because it’s a premium item, the rules seem to be slightly different – because if you don’t already have Burns, you can’t get Fruit-Bat-Man for love or donuts.

If you don’t have Burns yet and try to buy Fruit-Bat-Man, this is the message you get (but only after buying donuts):

So, new players, if you really want Fruit-Bat-Man, you’ll need to play a lot this weekend and keep your game moving so that you don’t miss out.