It should because who ever you bought the game should have a original digital copy so if your system ever crash and burns you still have a game to play. If you really need to know for sure.
Either call them or E-mail them with that question, that you will know for sure with out a doubt. I had Norton 360 on 3 PC's and one fried and I got a new one and I was afraid that I would not be able to down load it on another PC.
But I was and to make sure I E-mailed them and got my answer with in 24 hours. I hope this helps and Good luck to ya.