Can I add non-GOG game to my library? E.g. I've got Fault milestone one on steam, so can I add it to GOG library to use fault's wallpaper of the profile?

P.S. topic name should be additional, shame vocabulary

Hi, my name is Dessimu and I am an addict. I guess it all started back in year 2000 when I first laid my hands on Doom. Found the game on my father's computer while looking for incriminating material. The game, however... Couldn't eat, couldn't sleep, couldn't wait each day as so much did I crave for more DOOM!

...

Wait... This is not addicts group, is it? I guess I'll just go over there and quietly swig that free coffee.

...

As per OP question, I lack sufficient knowledge to provide an answer.

Thank you for sharing your story with us Dessimu. We are with you, loving you and believing in you..

You may add non-gog games manually to Galaxy but you will not get any free items like wallpapers or such this way.
To have them either wait if (it is always big IF) the game you're looking for will show up on GOG Connect or grab it from the store.

edit:
bloody links never work correctly..

So, BreOl72 answer was correct, you can't ; p

There's a wishlist request for this item if anyone would like to cast their vote for it:

https://www.gog.com/wishlist/galaxy/add_non_gog_games