Keyless start cars (e.g. Volkswagen) have a way to start with a dead fob.

If you hold the dead fob against the little key symbol on the steering column it'll power the fob by induction and you'll be able to start the car.

You're right, older fobs that just do keyless entry may not be able to start the car though.

It will, as most car key fobs also have a RFID in them that the car can read close range (e.g inserted)

It may not start the car, but will it at least let you put the car in neutral?

The poster a couple levels up said people where paying full towing price to have cars moved 5m. If you can put the car in neutral you should be able to push it that far yourself.

They certainly do. The 3-4 different Audis I have driven all have key cylinders in the door handles and a physical key in the keyfob. And you can start the engine when the keyfob is out of battery because they have a passive RFID built in the fob that the car can communicate with when the keyfob is inserted in the slot in the dashboard.