Depends entirely on the musician. If it's someone really well known, then it's going to be a lot harder, especially because they may be a bit pickier with what other projects they want their music attached to. They will often require some sort of licensing fee as well (especially if they are with a major record label).
Other artists, especially if they are still trying to get their name out there, won't necessarily care as much.
It may not be that easy to get permission to use copyrighted music for YouTube. It may take a process since there are factors that would need to be considered like the genuineness of this as well as protection of rights.