Yeah, you won't necessarily know it's working right when you plug it in because there's nothing "running." You'll have to feel the evaporator and see if it's getting cold. That's my experience with the fridges in the RV's we've owned, and I also had one in my college dorm room (against the rules, so silent operation was a bonus). All three of these fridges had freezer compartments that kept ice cream and popsicles firm without the refrigerated area becoming too cold.
That's a really cute little fridge. Kind of an old school cabinet with a transitional inner door. Plug it in and if it works, enjoy it!
Oh, and btw, do you see a gas fitting anywhere on it? Great for camping if it has one.
Ralph