No, this is exactly not the purpose of MonoGame.Forms.
To quote the headline of the readme file:
MonoGame.Forms is the easiest way of integrating a MonoGame render window into your
Windows Forms project. It should make your life much easier, when you
want to create your own editor environment.
So the purpose of MonoGame.Forms is - for example - creating your own editor tool, which needs a rendering window, for your own game.
This could be a level editor or a particle effect editor for example.
You basically create a new WindowsForms project and then add the MonoGame.Forms library to this project, to make the rendering capabillities of the MonoGame.Framework available in your editor project in a very easy way.
Also what @KiloMikeCodesStuff said should be possible. Creating your GameBoy emulator with MonoGame.Forms should be very doable, when you know how to render your contents using the MonoGame.Framework. Everything else is just the usual business of WindowsForms (working with a complete GUI solution for projects like that).
I also reccommend reading the README file and the Wiki (which describes the class library) to get a better overview.
Regarding developing games inside MonoGame.Forms: Yes, it's kinda possible. The library has native Keyboard and GamePad support of the MonoGame.Framework as well as RenderTarget support. However it only supports the Windows platform and I have never tested things like fullscreen support and different resolutions (but it's possible to resize the render controls), because - as I said - this is not the purpose of the MonoGame.Forms library.
I recommend using the MonoGame.Forms library for tools and editors only. Not for whole games on a bigger scope.