Can I wire my GFCI outlets in series with another GFCI?
Check out the drawing below. In it, we can see how the outlets are to be wired. Let's call the first outlet the "Parent" and the second the "Child". If the Parent outlet GFCI trips, it will cut power to the Child. Therefore it's important to know where the Parent outlet is located so that it can be reset if needed.
Outside of this instance, connecting a Style Drawer to a GFCI outlet shouldn't be a problem.