As for the real-world functionality of your donation, a car must also have a free and clear title to be transferable.

In some states you can request a duplicate title be sent to you in the mail, though it sometimes takes several weeks to get the process rolling along with a call for a tow truck.

When you call to begin the process of donation, a car and truck specialist will get a good idea for what needs to happen to your car.
If it's decided based upon the condition and usefulness of the car that it should be saved, a charity that will return it to good working order.
Otherwise, you can expect to to become parts.
Rarely are cars simply crushed for their metal, though this is sometimes done in severe cases.