How Long Can You Drive With A Blown Head Gasket Once You See Smoke?

Possibly forever. It depends on how much smoke, the police will pull you over if its too bad!

And it also depends on how fast the leak is, you must be able to keep the coolant and oil full or the engine will stop for good.

And there is a good chance that there will be more damage, maybe a cracked block or head if  you let this go on longer.