Since the anti-virus software needs to work differently with each OS, and, the boot process takes your system down to nearly blank, you need to load the software during each boot in order to be protected. If you only have it installed for one OS, you will have no protection in the other OS.
If the partition where you have installed the AV software is visible to both OS's, it may be possible to have each OS use the same installation of the software.
I also believe that Norton AV will workwith XP, but you need to install the Windows XP updates, and some patches from Symantec.