I believe all the electric accessories use the 12V battery just like a normal vehicle. The 110V outlet is just a small inverter, which is why it has a 150W limit - this is fine for laptops and phone chargers, even a TV, but won't power high-drain things like hair dryers or vacuum cleaners.

I don't know how much juice that blanket will draw, but I don't think you'll even have to put the ignition on accessory because the 12V plug next to the 110V is constant power (the other one on the right side of the dash console is switched power though).

This brings up another question... what happens if we drain the 12V battery? Doesn't the ICE start up using the HV battery?