I have tried 1080p output from xbox 360 to the same display you have and it works. No, I am just kidding it doesn't work.
Even though the xbox 360 can output 1080p games through component. I don't think the pioneer 5070 will accept 1080p through component. After all it is a native 768p display. It will probably only take and process or down convert a 1080p signal through the hdmi inputs. So, if microsoft ever adds the hdmi cable then yes it will work. Although, I doubt there would be a benefit to it. I have heard some folks refer to 1080i being the equivalent of 540p which would explain why this 768p display has no problem with 1080i (540p) sources. Happy New Year!