Will a degree turn you into a background singer, opera singer, or a singer? No, but it can certainly help you with building that network of contacts. Particularly those with an interest in musical theater, it takes time to learn how to hone your craft properly. Vocal lessons, music theory, and pedagogy, are all going to feed into making you a better artist. Making a visible commitment will help to set you apart from the crowd. It also provides you with insider information with regards to auditions.
If your interest is in being a music producer, then you will have heard the stories about those self-taught producers. If you want to be up to date with all the latest production techniques, then academic training may be worth your while. If you’re a lyricist or a songwriter, then further training can help you focus on developing your lyrics, as well as in arranging compositions.