Are you honest with your question?
it is a pretty honest actually... the Steam overlay function is not directly tied to Steamworks or Steam DRM and such, it is simply a feature of the client software; as long as the game is launched
via Steam, and is rendered with a supported graphical engine, it works.
That means that you can take a GOG game, or any .EXE that you like for that matter, add a shotcut in the Steam client, and after launch you can access Steam overlay and its features (chat, integrated browser and so on)...
It does not work 100% of the times, one know limitation is , for example, with games that start with a launcher before switching the main EXE, but it usually do
I've personally tried it with Legend of Grimrock, GOG version, and OOlite, the open source Elite remake, and it works perfectly Edit:
found a more specific quote
"The Game Overlay will work with third-party non-Steam games which you have added to Steam. The basic requirement is that the game uses Direct3D 7, Direct3D 8, Direct3D 9, Direct3D 10, or OpenGL for rendering. Some 2D games which use DDraw or software based rendering methods are not supported (ex/ Diablo)."