Will my xbox 360 play in 1080p through a CMP cable?

I have an old xbox 360 from before they put hdmi outputs on the back so i only have a CMP cable. My current tv is only HD ready so the CMP plays 720p fine. Problem is i am buying a new Full HD TV and was wondering if the CMP cable will output the 1080p resolution from the xbox or not. I have heard that this can only be done with the HDMI cable as the CMP can only go up to 720p. Any help would be much appreciated.