Does Parallels Desktop support hardware virtualization for the client VM?
As the comments have suggested, Parallels does not support Windows XP Mode in Windows 7 directly.

Parallels Knowledge-base article

However, the VMware knowledge-base does list a pair of patches from Microsoft (x86 patch and x64 patch) that remove the requirement for the hardware virtualisation on XP mode which should allow Parallels to also run the XP mode.

VMware Knowledge-base article