Yes. The halachic issue is hasagas gvul. If downloading it from youtube will not cause you to not purchase a song that you would have otherwise purchased if you didn’t download it, it is permissible to download.
(I’ve seen others say that the halachic issue with copying is dina d’malchusa. Even if they’re correct (which is a machlokes), there’s no problem of dina d’malchusa in the above situations where the law exempts fair use copying, as previously described.)