I see how one wire goes from that switch to the Xformer, another wire to the control board, another to the battery. I can't make out from the pic what kind of switch it even is, single pole, double throw? It would be bizarre for it to connect the Xformer to the battery, as there is no rectification there, ie it's AC. And "set exercise" would seem to mean that all it does is enable the weekly startup, or somehow let you program how often it does that.
IDK what's going on, but from what I see, I agree it's not clear that it does maintain the battery. I'd say more likely it doesn't at this point, but then who knows. You would think having the generator maintain the battery would be a standard feature, important to have, easy to implement, etc. So, I would think they would all likely have it, but as I said, all I know is what you do, ie that some of them definitely have it. D's is an older one. The one I have experience with is under 10 years old.
It really doesn't matter, more of a curiousity at this point.