(I know, late post, but..) To answer the original question more fully:
It may not be the most efficient or smartest way to make a PC work, but yes, you can swap out the HDD in a PC as a method of booting multiple OS's. You can even take a HDD with an OS already installed and swap it into a new PC with relatively little worry. It is normally very simple and surprisingly reliable.
I do this on a regular basis when toying with my spare boxes or when recovering data from laptops with dead screens, and many of my current toy PC's are running on HDD's with versions of Bodhi that were installed while the HDD was in a totally different machine from its current host, yet the installs all work just fine as long as the hardware isn't broken. Swapping out drives at random is almost always OK, though it can get confusing if you have many of them. The OS will normally detect most of the hardware changes and set itself up during boot-time to work just fine with whatever PC you've thrown the HDD into. There are exceptions, however. It doesn't /always/ work.
I only use this trick when a system dies and I slap the HDD into a new box or when I'm using very small old HDD's in the <10gb range. I think dual booting is a /much/ better solution to this kind of problem most of the time. If you're looking for the best solution to running multiple OS's, swapping drives probably isn't it. But that doesn't mean you can't do it.
Anyway, good luck with your PC build and I hope Bodhi works for you!