Would your car not start if it has a blown head gasket?

Would your car not start if it has a blown head gasket?
It'll start - it'll just overheat quickly.

It is possible that with a blown head gasket that under some circumstances the engine can become "hydrolocked". If the part of the gasket that blew out was between a water jacket in the block and the combustion chamber, and coolant got in to the cylinder and both valves, intake and exhaust, happened to be closed at the time, the coolant will fill or partially fill the combustion chamber and the engine will seize because the coolant will not compress and lock the piston in place where it was when the engine was turned off the last time.