I won’t comment on the Truma since I know very little about it. However, I caution you to not rely on just one electrical source of heat, no matter what it is. If the shore power fails for any reason, your trailer will freeze. Also the small amount of waste heat that radiates from recirculating hot water lines is not nearly enough to heat the full fresh tank, the cold water lines and the standard toilet, you need lots more BTUs.
We have discussed this many times, if you haven’t done a full winterization, you need two independent (and adequate) heat sources in case the primary one quits. You could try what you suggest, but leave the gas turned on and the furnace at a low setting, in case the water heater is inadequate or stops running. The problem with this scenario is that if the shore power fails, you will run down the batteries fairly quickly, unless the trailer is out in the sun with solar panels... It might be prudent to at least blow air through all the outside water ports and the outside shower, to limit the chance of one near the hull freezing.... and some sort of remote temperature alarm would let you sleep better, since you could keep a close watch on the inside temp and take action if it drops too low.
BTW, you have not filled out your profile or signature, please do so we know more about you. Are you being affected by the Bomb Cyclone? Be safe.
John Davies
Spokane WA