Knowing how many times a typical update requires power-on, power-off, and just moving the vehicle around the lot, it would definitely be inconvenient, if not impossible.
Update: they chose to use my backup code and they ended up using it eight times during the recall from the time I dropped it off to the time they gave it back. Probably sucked for them, but it only took an hour.
I did the same thing, so don't feel bad, my phone is my key (When it works).
The backup code is my backup key, until recently, when it all appeared to blow up.
The PaaK stopped working, and the backup key was blown away.
Lucky for me, it happened at home.