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I don't have a 360 to test, but I'd say probably not. The console requires controllers to use the Xinput interface (OUYA uses a modified HID interface), a proprietary 2.4 GHz wireless connection (OUYA uses Bluetooth), and it has proprietary DRM lockout, which OUYA's controllers would obviously lack.
I believe there are pass-through adaptors to make USB HID and non-approved Xinput controllers work (for legacy arcade sticks etc.) but at best you'd still have to connect through USB.
"But I don't want to go among mad people," Alice remarked.
"Oh, you can't help that," said the Cat: "We're all mad here. I'm mad. You're mad."
"How do you know I'm mad?" said Alice.
"You must be," said the Cat, "otherwise you wouldn't have come here."