This.
The battery is only for the transmitter for the keyless entry, doors, trunk, panic button, etc.
The security system uses a passive RFID that is energized wirelessly by radio waves from the transponder in the car. You do not need a FOB battery to manually open the doors or start the ignition using the actual key, and the security system should step aside automatically just by the mere fact that the real original key is in the vicinity.
I would just throw an extra set of batteries in the glove box. I agree though, that would annoy me to no end. Having to start the car in under a minute after unlocking it or it won't start? That's just stupid.
Just be thankful you don't have a Saab. If the batteries die in my fob it doesn't matter if I'm in the car, it will not start. The fob is the key.