Generally with a dorm style fridge, the watts required to cool the fridge will be close to the same for 120V or 12V. That is the amount of heat gain is a function of the box design and insulation
While the 12V compressor uses less amps when running, it will run longer then a 120V compressor.
OK there can be differences in the COP between 12V and 120V compressors. If your not changing the evap or condenser, the difference is not so great. I suspect that the overall energy use between a 12V and 120V dorm fridge will be close to the same.
Yes there are efficiency losses running an inverter, but it's not so bad. Lets not forget that the black box on the danfoss is an inverter (DC to AC) so no free lunches there.
As an example, my cheap $120 magic chef
120V 3.5 CF fridge pulls 15 amps when running off the inverter, which it great gobs tons of load But it only runs 10 minutes ish per hour (4 times 2.5 ish minutes). So while its moving lots O amps when the motor
is on, it's duty cycle is much lower then a 12V compressor. Average hourly load is 2.5 amp-hr or 55- 60 amp-hr in a day. A 12v compressor with variable speed, might get that down to 45 amphr. A difference of ~ an amp per hour.. OK it saves energy but at a cost.
My 120V fridge and a cheap inverter combined cost $200. It's been 9 years now and still going strong. BTW I am at anchor
and have traveled 200 miles in the last two months or so.