Yes, your hard drive will be OK.
And Yes, you will need to install drivers for all the new components, and deinstall the drivers for the old components.
Yes, Windows will autodetect the new hardware, and there is a possibility of blue screen of death. You should first deinstall all drivers on old computer (especially IDE controllers, VIA service packs, Intel Storage... if you have such elements and move from one to a different one), but also video cards. You can get sometime from producer site a small .exe (few Kilobytes) which deinstall everything related to the video card (Matrox for sure, S3 as I remember).
Then moe your hdd and install drivers for new components.
Timewise, you will finish faster reinstalling Windows, but you may have many applications/ settings/ e-mails etc.
If you get errors at loading, blue screen of death etc, start it in safe mode. Do all deinstalling before the hdd move, and have everything you could need copied/downloaded on hdd before the move. (you may not have CDROM access until you install IDE controllers etc).