I've been able to restore the license on a few of my games purchased on Ouya when I added them to the MOJO. So, yes they can still be played if they are available on MOJO. Some will be harder than others to get working though, as not every game has a restore license option built in. That could mean contacting Ouya or the game's developer.

As for buying new Ouya games on MOJO, you need Ouya cards as Kaimega said.