I tried. The app will show the splash screen and crash. It isn't a matter of it not being from the play store either because I have the play store on my ouya. A shame really because I bought it in hopes of getting it on ouya. The only other device of mine it works with is a galaxy s3 with a busted screen.
I tried sideloading it after I installed AOSP 5.0 - Good news. It launches the game. I'm still having trouble with AOSP, so i didn't do much, but it seemed to play ok.
EDIT: I think i figured out why it crashes at startup for other roms. So when i got it running initially on AOSP, it had my ouya plugged into a 1920x1200 monitor and i don't think it knew what to do, so it was running at like 640x480. I then plugged in my ouya to a tv and it started at 1080p. When I tried running Kotor again, it crashed at startup as reported by others.
I added the following to the ini file in /sdcard/Android/data/com.aspyr.swkotor/files/swkotor.ini under [Graphics Options]
Height=480
Width=840
This will allow the game to run. I played for a while, and it seemed ok. It is a bit slow, so we may want to try a lower resolution. The ouya may be getting too dated to play this very well.
One problem I ran into is that the ouya controller doesn't seem to be mapped correctly on AOSP. the triggers were mapped to look left and right as well as switch characters and pause. You have to hold the left trigger half way down to stop the camera from moving and hope it doesnt pause the game or switch characters while you are playing haha. It would be frustrating playing for too long without a fix.