First off, let's correct your terminology here. You have a true fuel regulating mix screw, not an air screw. Some other carbs, like the aftermarket VM slide type, do use an air regulating screw instead, but all the 650 CV carbs have a fuel regulating type mix screw. It helps to know which type you have because that determines what turning it in or out will do. Turn a fuel regulating mix screw in and you cut fuel flow, making the circuit leaner. Turn an air screw in and you cut air flow, making things richer.
Now, to answer your question, the mix screw adjusts mainly your idle circuit but may have a limited effect on the lower part of your midrange. To deal with problems in the idle to midrange transition area, you usually need to do some tweaking to both the idle and midrange circuits.
Something else to keep in mind is that the idle circuit never just plain shuts off, it's always flowing, adding a bit to the overall mix throughout the RPM range. It pays to get it right.