I seriously doubt that. If it is actually going straight through and coming right out the tail pipe you have more worries than just a head gasket. Put coolant in. Does green come out the pipe?
There is no way it is coming right out of your radiator, through the block, and straight out your pipe. If your motor is that bad, you would be smoking like crazy. Fill the neighborhood with white smoke crazy. You would also have NO power and it would be running like crap.