Not really - even though a lot of stuff on Youtube might have been put up there illegally, it's a public platform and you can download anything you like - not your problem. I never download myself, but instead simply watch or listen to stuff put up there. I've found over the years, watching many movies, that some are often removed only hours after I've viewed it - usually a note saying something about illegal blah should have been here and blah etc. Too late for those who have already downloaded the movie have got it forever and can transfer it to disc and keep it in their collection for that dull day on the TV when they can see a movie instead.
Here's a sample of what I mean - this is what you get here in UK when you try and watch a movie called "A Man for All Season" made in c1966 about Henry VIII and Thomas More.