I have a couple of the TM Alpha boxes myself and they are great starter boxes. My Alpha boxes are over 4 years old. I have had to lube the motors once, clean the contacts once and change the rubber wheel once. Almost everytime I have seen somebody burning motors in a starter box it is because of improper alignment. Nobody admits to it, but that is the #1 cause that I have seen. The only reason I switched to the Hudy box is sponsorship reasons. The Hudy box is great as well.
To answer your question, I don't see how a 12volt battery will fit into that box unless you get a 14.4v lipo. I ran my Alpha on a Losi lipo battery for over 18 months before switching to the Hudy box.