I had a similar situation with a tenant's mower. It wouldn't start, so she filled it all the way up to the top of the dipstick tube with oil. :confused2:
I drained the extra oil, took the muffler off, and let the engine run a while without it to clean the oil out of the combustion chamber. After soaking the muffler in carburetor cleaner and letting it dry, I put it back on and ran the engine until it stopped smoking.
Short answer, yes it will smoke like a fog machine until the oil burns off.