It's cheap, buy one and try it at home.
IMO - The 120v unit should work fine. Engine running, shift in park. It will take 2.5 amps from the inverter and the inverter will take 25 amps from the T4. The inverter is on a 40 amp line and fuse.
I expect the alternator will keep up and the battery will not be discharged. If concerned, run it for another minute after the heater is finished.