Depends on the bios, but generally no, you just need to be able to select it as the boot drive.
Note that you may not be able to boot up the OS espically if its out of an OEM pc like HP. They are often tied to specific motherbds and wont work unless they see an accpeted model#.
Also it may not boot if current hardware is to different than previous hardware. This is something you can usually work out though.