Yes a bad head gasket can cause smoke from tailpipe.
If your head gasket is bad it can either leak coolant into the cylinders or leak oil into the cylinders depending on how bad the head gasket is blown.
The head gasket seals off the cylinders and coolant ports to keep the coolant and oil from mixing and to prevent coolant from burning in the exhaust.
If you notice coolant loss or notice white smoke from the tailpipe then your head gasket could be blown and allowing coolant into the cylinders which is not a good thing.
You'll not only lose coolant you'll also get coolant into the oil which can damage your engine.
If your head gasket is blown and allowing oil to get into your cylinders then the engine could burn oil.
If it's burning coolant then some head gasket sealer can usually work to seal the head gasket but if the head gasket is blown where oil is leaking through then the head gasket needs replaced.