I usually ask my students during flight what would happen when I pull the primer out and push it back in. Usually I get a big question mark, sometimes they tell me the engine will quit.
The truth is that nothing will happen when I pull the primer out, and I mean absolutely nothing, also in a warrior. The problem comes when I push it back in, since now I have excess fuel going to the cylinders.
I mean try it, and you will see, just be carefull when you push the primer back in, so you wont flood the engine.