** I have recharged my car's air conditioner. Can I do the same with a dehumidifier? **
Properly? I doubt it.
First, there are no access valves on domestic refrigeration appliances. They have to be added when necessary for repair.
Second, a specific amount of refrigerant has to be added. You do not just dump it in until you see it in a sight glass (as there is none). Proper charging requires a special tool not usually used in automotive service.
Third, such systems are sealed and will not leak refrigerant unless there is a hole in it somewhere. It is useless putting refrigerant into such a system unless you can find and repair the leak first. Doing so could also be against the law... depending on refrigerant type. Most people wouldn't have the tools for leak checking even if they had a can of refrigerant laying around.
** Would it use the same refrigerant as a car? **
Maybe. The refrigerant type and amount should be listed ion the appliance's identification label.