I don't have any experience, but I think even though it is heated, humidity could be a problem. A Plastic tarp doesn't breath. During really damp weather, could condensation form under the tarp? That said, when I lived in a condo years ago, there were three levels of parking, (drive-in ground plus two lower levels.) The lowest level was always bone dry in the winter.
IMO, if you're willing to pay for heated parking, I'd spring for a proper car cover.