A couple comments are in order here.
 
First the fuel solenoid is not intended to be a fuel flow control other blocking the main carburetor jet(s) during to prevent raw fuel from entering the exhaust which results in a loud report. It has nothing to how fuel flows from the fuel tank. This is the job of the float needle valve and seat. This is a misunderstanding many DYIers have about the purpose of the solenoid.
 
Second the white smoke was most likely just oil burning off in the muffler due oil overflow from the crankcase due to fuel polluted oil. Usually take 5 to 10 minutes burn off once the muffler is hot enough.
 
Now if the crankcase was overfilled then you most likely have a leaking needle valve/seat problem and it would still flood out the engine. If you have a Nikki carburetor the fuel bowl gasket can also cause fuel overflow in the carburetor as the part of the gasket or separate o-ring depending which version was use can leak. As the fuel overflows in the carburetor it work its way through the intake system into the cylinder which then leaks pass the rings, polluting the oil