Is there any SDK I can use to write a console app that can connect to an Xbox 360 as a controller and simulate controller interaction?
I don't exactly have a turnkey answer to your question, but a BeagleBoard would be an ideal piece of hardware to use to simulate input.
It can act as a USB Host or Device and you can program it to appear as any Device.
You could easy capture and replay controller USB traffic to have repeatable input, or go the route of scripting the events yourselves. Unfortunately, I don't know of any existing project to do so.