No!
You can still use your car. But you will need to use the metal key in the fob to lock and unlock. To start the car when the battery is dead, you need to hold the fob next to the stop/start button, then it will let you switch it on. Mind you, the car will be drivable but there will be all sorts of warnings, namely key not being detected, etc...
It's dead easy to change the battery though, and you can switch off smart entry / remote start, etc from the dash, and buy yourself a faraday pouch for your keys.