12V plug on Antenna Booster Wall Plate Constantly Active?

The button and the light are only for the signal booster. The socket remains hot all the time, with whatever voltage your batteries can supply. Whether it can run a C-pap I have no idea.

Also, I've tested it, and convinced myself that the signal booster pulls so little current, it won't make any tangible difference in how long you can boondock. I don't remember the current draw, but it was tiny. Of course, I fully understand saving every spec of power when you can. But don't sweat over it too much.