Possibly; possibly not - you might get a partial thumbprint off the button, but you wouldn’t necessarily get classic ‘dabs’ off the handle - more likely a print/smear of the intermediate phalanges (the middle bone) and the palm as the hand wrapped around it. Similarly with the steering wheel and (possibly) the handle to move the seat back. The most likely locations for actual fingerprints if the car was opened and pushed would be the underside of the driver’s door handle (to open the door) and the top right of the windscreen (pushing with one hand wrapped around steering wheel and one hand on pillar).Wouldn't his fingerprints be on the handbrake though?
That said, you would think police would be aware if this was the case, unless RM (the garage owner) belatedly realised that he might have destroyed vital evidence by moving the car and decided to say nothing.
But my point here mainly is that sometimes confusing aspects of a case stem from mundane and unrelated causes - as with the Valdez case, where the ominous “HE IS NEAR - HELP ME” message on the car’s rear windscreen turned out to have been written by teenagers who discovered the vehicle before it was reported to police.