If you have a hard drive with one or more NTFS partitions, then yes, in my opinion it is very likely that Knoppix will corrupt the partition if you write to it. You may or may not be aware of the corruption immediately, you might even save a lot of important stuff and think that things are working just fine, but the corruption will eventually catch up with you. I say in my opinion. Many other people have reported corruption from writing to NTFS. Some people claim it is now safe. I don't believe it and feel my data is too important to risk. If your data is less important and you don't want to hear this, then give it a shot.

Knoppix can write to the various FAT partitions just fine. But the default nature of Knoppix is to mount a partition as read-only, to prevent novice users from destroying their data and then blaming Linux or Knoppix. If you want to write to such a partition you must make it writeable. Prior to version 6 this could be done by right-clicking on the partition icon. You can also use the remount option in the mount command, see man mount for details. The right click approach may not work in 6.x (lots of things don't work in 6.x), but the mount command approach should still work.

If you want to back up files to a NTFS drive I strongly suggest only writing to it with Windows (and even Windows often will corrupt a NTFS drive). For such recovery with Knoppix I boot Knoppix on the failing Windows system and transfer recovered files across a network to a Windows box, which I have write to the NTFS partition attached to it.