Mostly yes, but it might need a slight adjustment.
For example, if the ordering of the drive is different (i.e. hdb instead of hda) you will have to edit a couple of files to fix them: /etc/fstab and your bootloader config file, usually /boot/grub/grub.conf or /etc/lilo.conf.
You can do so by booting from a livecd. Use fdisk -l to see how your drive is called and then mount it on any temporary location and edit the relevant files. For the rest: it should just work. I assume you are using a pre-made kernel. Most distros compile them with everything enabled, so your chipset support will be already there, unless you are using a custom kernel. In that case, you must recompile it with the support for your chipset enabled.