If its going on a wrecker I would not worry about it. Most good wrecker drivers are used to dealing with severe damage and cars that are not able to roll onto the bed by themselves. Some other tow truck drivers that are used to dealing with illegally parked cars and repossessions are experts at sliding a car up onto the bed of a wrecker with no noise or damage to the car.

Of course if the car is going via transport this is an entirely different thing. Most transport companies require the car to be driveable because they physically drvie the car up onto the truck that is transporting it.