Just to clarify, since no one else has:
GOG Connect is a promotional program that allows GOG and their partners to make games available to redeem on GOG if you already have them in your Steam account. Each Connect promotion is time-limited, but any games redeemed through it are in your GOG library for good.
Galaxy 2.0's "all your games in one place" feature works differently. It's basically like a more advanced version of the Steam client's "add non-Steam game" feature -- the game will appear in the launcher, but it won't be added to your library, and I doubt it will even show up in your GOG user profile on the website.
I apologize if you already understood this; the topic title mentions the magic word "connect", and there have been A LOT of posts here and elsewhere on the Internet over the years by people confused about how GOG Connect works. :)