Packocrayons, Yes, but then there is no way to remotely track the dog, only the collar. So you may only get one ping at your house. My idea is to fool the thief into thinking the collar has no transmitter, so he will bring it with him.
Javaman, I was thinking the collar will normally send a location every x minutes, whenever it is away from the house. This will help if the dog escapes and runs away on it's own too.