Does PaintCode generate images or drawing code for UI control states (like button normal, pressed, and hover states)?

Yes, it does if you use variable or expression feature of PaintCode in your design.

Please, check out the "Button" canvas in the "Example.pcvd" document ("TabBar and Button" tab) in the example project. Look at "selected" and "highlighted" variables in "Variables" group of Library and on how StyleKit drawing method is used in viewWillAppear: (Swift: viewWillAppear(_:)) method of EXTabBarsAndButtonsViewController subclass.