Yep the above advice is correct, the system may boot from the nominated drive (BIOS) but the installed software (and referenced data) will have absolute references to the drives (hd<a><i>), and they would have to be identified and changed manually.
If you go down that road, then I suggest that you boot the system with a Live CD/DVD linux, and then perform global searches for references, but that will not cover any software applications that have been built (compiled) containing absolute references (picked up from system data during a build, or manually specified).
In short, my opinion is that you are always better off in the longer term (many considerations) if you store your valuable user data on a separate physical drive (yes I know that isn't always possible, but more often that not it is
), so that if you perform a change of physical drives, or drive order, you avoid this situation.
In this case I would recommend backing up your valuable user data, and performing a fresh OS and application software install, then restore your backed up user data. The other advantage of this approach is that you will have (a) a complete backup copy of your data, and (b) proven that you can recover/rebuild your Linux installation. Both steps of which would be required if you (heaven forbid) suffered a system of hard disk failure) in the future.
Hope that assists.