This is an especially common question because ultimately that's everyone's real goal: to get a job. So will an internship get you there? Maybe, but probably not. Getting a job directly from an internship requires luck, good timing, hard work, and patience. It tends to be a matter of being in the right time at the right place when the company happens to be hiring (usually to replace someone who was promoted or left) and you've put in the work to prove yourself. Sounds difficult? Well the alternative isn't easy either. Everyone tells you how hard the industry is to break into and I'm sure you're sick of hearing it because it is probably all anyone has ever said when you told them you planned to work in the music industry. It's kinda hard to miss that memo when your teachers, parents, aunts, cousins, friends, guidance counselors, etc. regularly tell you you're crazy and should pick something more practical. (That would be boring wouldn't it?) The thing is you can hear it a million times and still not be prepared for how difficult it really is. There is no one path, you have to forge your own like an explorer clearing the wilderness (excuse the cheesy analogy). You probably won't get past the application stage unless you know someone or have an incredibly impressive résumé. And the salary you'll be offered will be far lower than you were expecting. It may be lower than you can afford and it gets worse if you don't already live within commuting distance of the major city you're hoping to work in (unless maybe you want to work in Nashville since the cost of living is considerably better than that of New York and LA). You may apply for 100 different positions only to hear anything back from one or two of them.
What's this have to do with the question? Well an internship probably won't directly land you a job unless you're really lucky. And a really great intern. But it will make the frustrating process of finding a job a bit easier. It will give you people who can pass on leads. It will give you a name to write down when it asks if you found the job through a current employee (which will help get your application reviewed by more than computer software). It will give you a solid résumé that's worth them picking up the phone and giving you a shot. It will give you things to talk about when you're in your interview praying for things to go right so you can finally get the heck out of your parents' house and tell everyone you've finally made it. It will help you build a reputation and a list of references. It will prove that you love the industry and that you know what you're doing better than the guy who just thought it'd be cool to work with rock stars. And when the odds aren't in your favor, you've had more than your fair share of rejections, and your friends have decent salaries that are making you reconsider everything, the experiences an internship gives you will help you remember what you're fighting so hard for in the first place. Internships will make it a lot easier to cultivate the unique combination of knowledge, passion, connections, luck, and relentlessness it takes to get a job in the music industry and when you do, it will all be worth it.