The Kenwood stereos in my car have an option to (supposedly) shut off the subwoofer amp, but in reality it leaves the amplifier on but just cuts signal. Kind of disappointing.
That said, an amp that's on but being used only lightly isn't going to draw a lot of power. I probably wouldn't worry about it. You could easily find out with a multimeter - connect it in line with the amp power wire. NOTE that if you draw more than your multimeter's capacity (usually 10 amps), you'll zap it - so I would start at low volumes and work up from there to see how much power it draws at your desired volumes.
From there, you can estimate how much power this will draw from your batteries, and even figure out how long your batteries would last if you were just powering the sub (you aren't, of course, but it'll give you a measure of how much power you're drawing in the real world).
I have a Pioneer head unit in my camper, with Ford stock speakers (ugh) in the front and Pioneer 5x7s in the rear, one of which is buzzing and should be replaced. I don't have a sub in the camper...