Does the fuel enter the car when ignition is switched on?

I hope for you that the fuel is not entering the car. Specially if you are smoking...
If you mean entering the carburetter : once you switch the ignition key into "on", a small pumps starts filling up a small tank inside the carburetter.

:)

When the ignition switch is turned to ON, the fuel pump, located in the gas tank, will run to pressurize the fuel rail. The fuel rail provides the necessary fuel and pressure to the injectors.