Can I exercise XP downgrade rights if I currently have Vista or Windows 7?

No. Only OEM system builders can provide the "XP Downgrade" option. Velocity Micro only provides this option with the purchase of a new system.

This does not however prevent you from installing your own retail licensed copy of XP on your system.

See also:
Microsoft's Downgrade Rights Details & FAQ
Can I change the operating system on my computer?