I have the same engine. Assuming it has the same carb, NO!

The Screw in question does more that just "Stop" the rotation at a given point based upon its setting. As has already been pointed out it A: hold the barel in place, and B: acts as a guide pin for the barrel rotation, thereby ensuring the correct amount of side to side movement as the barrel rotates.

I have not ever tried to run mine without this part, and Im no expert, but I assume based on the way its put together that the positional movement is in fact a requirement for the low speed needle valve to operate correctly, and the mixture to remain constant as you open it up.