Of course knoppix can be installed to the hdd.
Heres where you'll usually find good advice on how it's done.
I found it had no problems when I had it installed - though it's fair to say that some have reported problems, personally I just made sure that I changed the apt-sources so that they reflected "proper" debian ones once it was installed, then it was just a case of looking out for any config issues.
After a couple of updates/upgrades, it will have pretty much wiped out virtually all of the knoppix specific stuff, and I found it a very much easier way of getting debian onto a system - "proper" debian can be a bit of a bugger, as large amounts of it have to be done manually, so if you're unfamiliar with CLI, it's quite a good way to go.
regards
John