it should run. It may have to sided loaded at first. the only question is how well the user interface will work with a controller. It should be navigable if Sixaxis Controller and app are any indication.
I put Netflix on mine. Without changing the key mapping (which might interfere with games), the gamepad didn't work too well with Netflix. I had to just use the trackpad on the gamepad to use a mouse cursor.
I know we're just speculating about capabilities at this point, but does anyone know if the Ouya will be able to run the Netflix Android app? That would be a huge if it could.
The biggest problem I've noticed is the stream quality on Ouya. I've connected mine via Ethernet and (maybe others can confirm with Netflix) the stream seems very poor, especially on a large screen. For example, streaming Foxsoccer2go on highest quality on Ouya looks MUCH worse than running through my laptop -> hdmi port on the TV. Unless there is some kind of method to improve this, I would not recommend streaming on the Ouya.
XDA Developers was founded by developers, for developers. It is now a valuable resource for people who want to make the most of their mobile devices, from customizing the look and feel to adding new functionality. Are you a developer?