Nope. You need to have purchased games to be able to play them, downloading a free game counts as purchasing. I know this because in the first few months I had PS+, I didn't download every free game every month, and when I later got back to those games to download them they weren't free anymore, if I had just bought them (for nothing) I would've been able to download them later, even when they weren't free anymore.
The reason you are allowed to play them now, is that your brother bought them and you have a secondary account on "his" playstation. This will change when it's no longer "his" playstation, but instead it's "your" playstation. Then he will be able to play your bought games, similar to how you can now play his. Hope that makes sense :P