No, it will not cause smoke from the exhaust pipe. However the leaking oil can drip on the exhaust manifold where it will be burnt and smoke.
Burning oil
Stuck or broken oil rings can cause blue smoke.
If you nicked the oil pan it could cause it to smoke from engine area. Is the smoke coming from the exhaust or engine bay? If exhaust, then I highly doubt it was caused by the curb incident.
Dont filled oil so that no smoke
blue smoke can be caused by sticking valves or burnt rings
Depends: White smoke=Coolant entering the combustion chamber. Caused by blown head gasket or cracked head. Blue Smoke=Burning oil. Cause by worn or broken rings. Black Smoke=Overly rich fuel/air mixture.
Blue exhaust smoke is burning oil.
what kind of gasoline are you running? and what color is the smoke?
valve seal
Moisture in the exhaust, or a cold running engine.
Coolant getting into the fuel or oil.