I think the in-game overlay is the preferred method for debug stuff. With the in-game overlay though you can make it possible to toggle it with a keypress if you wanted.

It should be possible to programmatically create a console window. So if you create a console-less application then you could conceivably create and destroy (or at least hide) a console window. It would require platform specific code, and I can guess that it won't be pretty. You'll probably have an easier time, and get better user-friendliness from, creating your own in-game console. Of course, Peter Wang's solution is probably best if you don't need an interactive console (assuming whatever that is isn't interactive).