Is this wrong? I wouldn't download them, and I don't think it's illegal to only view them, but would I be culpable, since I might be encouraging whoever posted them illegally? Is there anything from the catechism or Scripture, or other Church doctrine that can apply here?
There are no explicit Church documents that spell out what to do in every situation of copyright infringement.
I don't really see a difference between illegally downloading a copy of a movie or TV show and simply viewing an illegal copy (such as one posted on YouTube). Either way you are consuming the work of another without honoring the methods of distribution for that content which have been put in place.
You know you cannot go wrong by sticking with the stuff that is legal.
Stick with that which is legal...and otherwise moral.