Considering how the PHONE, not the WATCH is paired with the car, I'm not confident that you can pull that off.
I can't count how many times I've had to wait for my phone to connect (remotely) to my car to unlock it. I suspect if your watch had to connect to your phone and then the phone had to unlock, it could be a long wait, up to a minute or more.
Also, since it's not legal to drive without an drivers license, leaving the key card in your wallet takes care of both those requirements.