So the 'factory' Sony car stereo in my RV was a mess of buttons and knobs and at an awkward angle to look at to figure out what station I was tuning in on XM. So I replaced it with a nice touchscreen that I think will really help minimize the fuss while driving.

My question is this: the stereo is NOT keyed with the ignition. I suppose this is so one can listen to tunes throughout the RV when camped out. I can turn the monitor off, so other than the stereo memory, the only powered thing I see is one lit "Home" button. Am I correct in assuming that this will NOT kill my battery if I'm swinging by every couple of weeks? LOL

I think you should be fine. If not the case, wire a rocker switch in the power lead for the radio, and manually cut it off when not in use.

In the idle mode you should be fine.
I don't know how long it will last with a bunch of amps and pushing them for an extended time though.