Yes, but...

A video with music contains three copyrights: the video images, the sound recording, and the underlying song composition (music publishing rights). In a video where you are performing a cover song, you might control the copyrights to the video images and sound recording but don’t control the music publishing copyrights. To use the song composition, you need to negotiate a synchronization license directly with the music publisher.

However, many music publishers have entered into license agreements with YouTube permitting the use of the songs they control in exchange for a percentage of any advertising revenues (although in some cases the publisher may set a policy that a particular song is blocked from use). As a result, in most cases, YouTube has already obtained an agreement with the music publisher. To determine whether or not a publisher is participating in an agreement with YouTube, please contact the publisher directly. Publisher contact information may be found at ASCAP or BMI.