No it will not, because the device requires a display driver. Generally the Xbox 360 USB ports should not be used for powering devices such as external hard drives or this since the required ampere draw could damage the game consoles internal circuitry over time. turbo coolers (extra fans that use USB power) are another item to avoid. Additionally this display product works best at resolution multiples of 1366x768 while other scaling factors result in poor display quality.
Example: a Samsung Netbook with a 10" screen plus this looks fantastic. In contrast 24" HD monitors in combination this display cause this display to dither colors drastically and appear washed out otherwise. Any display that supports HDMI provided the XBOX incorporates an HDMI port Will work. BenQ is one brand used at tournaments.