Games are not permanently available through
GOG Connect, but only for a certain period, and only when GOG and the publisher(s) agree that it's a good idea. At the time of writing, there is one game available - AI War 2.
Connect your accounts and remember to frequently take a look at the linked page above. If you miss them, you can
hope that they become available again, but there is no telling
when (or really,
if).
Galaxy 2.0 (from what I've read, I don't personally use Galaxy at all) simply allows you to launch non-Galaxy games (not add them to your GOG account), similar to how Steam currently allows you to add non-Steam games to your list and launch them from Steam.