Nope! You do have to install Parallels on your boot partition, but the app doesn't care how you've got your disk set up - even if you've partitioned it for Apple's beta Windows solution, Boot Camp. You can even create the virtual machine on a different partition if you don't want it hogging space on your main drive.

Bonus Parallels tip: If you need to use Windows on a Mac other than the first one you installed and activated Windows on via Parallels, simply install Parallels on the new Mac and move the virtual machine file (the honkin'-big HDD file) from the old Mac to the new one. Windows will think it's still registered since it's on the same machine - a virtual one.