Hi Steve,
the API gives you the eye-gaze point on the screen in pixels, and there are functions in the Windows API that lets you set the cursor position. So yes, this should be an easy thing to do.
EDIT: While it’s certainly possible to control the cursor using the eyes, it has to be done with finesse in order to provide an enjoyable, natural user experience.
We see gaze tracking as a complement to the mouse, not a replacement. The eye is more direct and natural for pointing, but less accurate since it is never still.
Gaze clicking the way you suggest can be a good use case for eye tracking as long as the accuracy is sufficient. (The EyeX Engine improves the accuracy by letting the gaze click snap to the nearest activatable interactor within range.)
Directly controlling the cursor isn’t recommended though. Imagine trying to read on the screen when the cursor follows your gaze point all the time. Not only would it obscure the text, you’d soon want to shake off that thing that is stuck on your eyes. Go away, you cursed cursor!