I took one of my Android games that had been happily sitting and being downloaded on the Google Play store for a year and built it on my Ouya ( when it first arrived ) and it ran with no issues and without any code changes ( its an OpenGL realtime game ).
All I had to do before I could release it on Ouya was to replace/comment out the touch screen controls and replace them with Ouya control methods ( which are all in the Ouya SDK that is free to download from their site ). I also had to build in Ouya's payment system ( again in the SDK and pretty easy ).
It was then accepted and published on Ouya without any problems.
If I had to do the opposite (i.e. I developed it via Eclipse with Android SDK on Ouya ) it would be just as easy. I would just have to develop a control interface that worked with touch screens ( which for a Joystick is somewhat more complex then just programming for the analogue controls of a Joystick ) and remove all the Ouya payment routines.
Please let me know if you want more detail.