If they have winterized, they put pink-stuff in the water lines. If they apply pressure (air) to the lines and if there are any leaks, the pink-stuff will spew out just like it would if it was water. So as far as that goes, I think everything is OK there.
The water heater will fire on gas, but if yours has gas-electric, you won't be able to verify the electric. You absolutely do not want to turn the electric on the water heater unless there is liquid in it, otherwise the heating element will burn out within seconds (like 5 seconds!) So you won't be able to test the electric.
If they are willing to unwinterize and then winterize again, let them do it. For your own peace of mind, and for you and their protection in the event something arises in the future.