My guess is that it will not.
In earlier descriptions about the keycard says that you tap it on the B-pillar to unlock the car, and the tap it on the console behind the cup holders to get the car to "start". With the very short range of the RFID technology in the keycard, I very much doubt that it would still see the keycard rattling around in the cup holder. I also recall reading that the presence of the keycard wasn't needed once the car had been started.
I'd suggest contacting Tesla to ask how they expect this to work, and don't let them off the hook until they give you a reasonable answer. They really need to consider the corner cases when they throw out a solution that's been refined over the past many decades, in favor of something new and shiny.
EDIT: My guess (prediction): disable your phone's bluetooth, unlock the car with the keycard, and use the keycard to start the car. Without the phone active, walk-away will be disabled.