Yes the solenoid will block the flow of fuel up the fuel pipe in the stem of the carb and was done so to help with backfire on shutdown. Not quite a perfect system, but that's its purpose. Because the carburetor bowl is vented at the entrance of the venturi, fuel does have another path to overflow should the float valve let fuel by whilst sitting however. Many engines today are not built with AB solenoids plus enabling a solenoid may or may not allow a backfire to happen. No other side effects.
After I wrote the 20 year comment I thought, that's nuts- I must be getting old because I remember the back fire being brought up in a early for me Kohler service school . More than 20.... It was actually cute because Kohler is one of those companies that seems to document anything. IE A simple part change comes with a sheet of notes telling you why and revised instructions and the like. Dealers brought up the backfire on Commands and the discussion went from the effectiveness of the solenoid to idling it down for 30 seconds to basically having the customer try various throttle positions at shut down to different fuel. Poor guy was frustrated. That apparently wasn't in his notes...