@blue jay,
yes you can get faster HDD (mechanical) units.
typically a laptop drive (2.5") has a RPM of 5400, but some have 7200.
a desktop drive (3.5") is normally 7200 but you can get 10,000 and if you have more money than sense there are even 15,000 units out there.
but with games, the bottleneck is not normally I/O speeds to the drive but with your GPU.
for my money, bite the bullet and go SSD. 250GB units are $AUD140.
and although they aren't a big improvement during the game, they will remove any drive bottleneck.
as to your original question, can you run the OS off the old drive and the game off the new drive - of course you can.
you only have to change the default folder location while you install the game to that second drive.
BUT... anything OS related that the game may do, like access Temp folders, pagefile, etc, will still hit the old drive.
so anything game related will go to the new drive, anything OS related will still use the original drive.