Yes, it gives a notice like “Copyright issue, still alright to use.” It’s then not possible to monetize the video (no matter the number of views, I won’t make any money), and one or more ads will play on the video. Also, at the end of the description YouTube says what music is used with an image and link.

Sometimes there’s a notice saying the audio will be muted in certain countries, and some music would not be allowed at all (Beatles and Prince, for example).

Vimeo is much more lenient with no ads, and I’ll often have a video up on both YouTube and there.