You can use the camera without the battery, but you can only use it in C mode with C, CT*, CF, CFi and CFE lenses in that mode. The mirror auto-return will not work either, so you will not get your mirror back in place until you advance the film. In other words, it will function pretty much like a regular 500 series camera.
As for the backs, as far as I know, the only difference in the A12TCC and the E12FCC is the darkslide holder you mentioned, and the age. The A12TCC is older. BUT, if you are talking about the E12 back, then there is a difference. Hasselblad made E12 backs for the 203FE and 202FA, and they do not have the zone system controls like the FCC and TCC backs. They still transfer ISO information, but don't have the zone system controls (which, honestly, I don't think I have ever seen anyone use anyway...I would just buy whichever was in better condition at a better price).