Can oil leak into cylinders thru intake manifold? misses on start then smooths

no just on startup longer it sets he longer it smokes and runs rough

Sure sounds like coolant instead of oil. A combustion leak test will tell. If it were oil it should smoke all the time it is running. Coolant seeping into cyl. while parked, then clear up after burning out of cyl. more likely. Oil leaking out of engine maybe? How much oil in how many miles?