No problems to play on the main screen with opengl when multiple screens are enabled would be a good idea…
Then why not multi-screen management inside OpenGL Games (ex: each screen on different camera view, on main screen for the game, screen 2 for the score board…)
This is not related to openGL.
Whether or not you can have multi-screen usage depends entirely on the OS that provides the rendering contexts. Windows, for instance, allows this(with most drivers). Please bother your favorite game developer to include this functionality.