yes that is the correct normal position to leave the solenoid in for when pushing in the key.
I will try and explain it a different way than Joe does, he is 100% correct of course, but this might help you.
when you have the motor running the fuel pump still sends pressurised fuel to everything, inc the solenoid ,but without the key pushed in the valve is kept closed so
no fuel enters engine from the solenoid.
if you pull a pipe off the solenoid fuel will come pouring out of it because it is getting that direct from fuel pump ....need to plug the pipe if nipple is broken ...
imagine a fuel line going from fuel pump direct to the crankcase, fuel would keep going in all the time the fuel pump is working.
Now cut that pipe and put in stop valve, this is the solenoid...it only opens when you push the key in !!!! without pushing in the key the valve is shut, this then lets
the carbs do their job an only them sending fuel to the crankcase.
When the red lever is turned up the valve is open for manual starting, then you need to hurry up and close it or will flood like Joe has said above.
i used to think it was like a small electric pump, it is not, it is simply a solenoid that opens to let fuel pass by.
this is also why you only hear the one lick, it is the plunger inside opening quickly.
hope that helps...
once you get the drift of this you can see that Joe is bang on the money with his explanation, but he forgets we are not all outboard Guru's like him ha ha