If they have not prevented you from booting the CD/DVD (by adjusting the boot order in the BIOS), then nothing installed in the hard drive OS will matter to Knoppix. Knoppix will have access to any standard USB port.
That is not to say that you should do this. You are using someone else's computer, and bypassing things that they have set up is a touchy subject. While it may make a lot of sense to not lug around a second personal laptop so you can have some private computing time with your choice of applications while traveling for the company, it certainly would not be all right to copy private company data to the USB with Knoppix (likely the reason they have a write lock-out in place). You know what Spiderman's uncle would say in a case like this.