Yes. You can boot the CD with or without a hdd installed. Of course, without a HDD there is nowhere to same files but in your ramdisk. I use wimpy 2gb hdd's and or small usb pens with an overclockix CD sometimes to amke it more functional and give myself permanent storage.
The CD has many tools to manipulate different filesystems. it can help you recover data if the hdd's OS has become unbootable due to corruption. It can resize partition on the fly, similar to partition magic, and it can image a drive.
You can also use a hdd to make it run slightly differently. For instance, you can create a persistent home directory, which allows you to save your custom desktop and program settings, your browser favorites, your folding directory, and any documents you create or files you download. A persistent home can be on unpartitioned hdd space, a fat32 partition, and on either a hdd or usb pen drive. You can make it use your custom settings when booting by entering a code (knoppix home=scan) at the initial prompt whenever you boot.
You can also create a swap file for it, if you have a hdd in the system. It can take a small part of a fat32 partition, or it can use unpartitioned space for a swap file.
A future release will allow you to copy most of the filesystem to a hdd, yet not the part that would go in the boot sector or install a boot loader on your system. In effect you could just stick about 2GB of files in a folder of any existing Fat32 partition, so you wouldn't necessarily even have to partition it, or do a full install. But it operates faster having its files uncompressed and on a hdd rather than compressed and on the CD. This technique is called a poor man's install.
There's also a newer installer script that has more options than the current one, that I'll work into the next release- Overclockix 3.3.