If I rip YouTube videos on my computer and convert them to a file format that is compatible with the iPod Touch 2 gen, and put it on the iPod, would it void my warranty?

Unlikely.
Warranties normally only cover the hardware and not what you put on them.

Well, the iPod touch's warranty is sensitive. It becomes a brick if you download illegal music onto it. Somehow it knows by reading the file. I really want some YouTube videos on it without connecting to a network, and without the warranty voiding.

Has anyone tried it before?