You can get by without it if you need to, but the bottom line is that your OS is going to reference files on your system drive at some point while you are recording and that will in turn impact the number of audio files that can be played and recorded at the same time, hurting your overall performance.
So, using a seperate drive for audio is recommended by pretty much every professional in the field, but remember that your audio drive is still being used a ton and is much more failure-prone than a seperate backup drive will be.
Case in point, I have two computers I use for Audio right now, a PC and an iBook G4. I use additional drives on both of these machines for audio, and I keep a folder on each drive labeled Audio, and I try very hard to keep the contents of these folders identical. A few nights ago, there was some nasty error while I was changing the share properties on my PC's D:\Audio folder and the whole partition and all the data was unreadable. The drive diappeared from "My Computer" and was only visible under the disk management utility, which viewed it as unpartitioned space. Fortunately, just the night before I had updated both the PC and Mac Audio folders, so I only lost a small amount of Data (one pro tools session that I had only been doing some experimenting with a digi beta product on). So in this case the extra drive was the one that needed backup. I simply do not trust hard drives to be reliable. This little adventure has convinced me to buy another large Firewire drive and to backup both Audio folders to that drive every night, and to only use that drive for backup.