No, it's not an input.
That's why it's called mini-DVI -> Video and not Video -> mini-DVI.
The mini-DVI port on MacBooks and iMacs, as well as the DVI port on MacBook Pros, Mac Minis and Mac Pros are strictly video-out only.
You can input video using the firewire port and the appropriate converter box if you want to import video from an analogue source, digital cameras plug straight into the firewire port and if you want to use your 360 you'll need something like the ElGato hybrid TV tuner which has an auxiliary-in port on it but then you'll still have some lag in controlling as the video is converted through the device.
But you can't input video through the DVI ports on any Mac.