There's a pretty detailed discussion of this subject
in this thread. It's worth revisiting, since that discussion is from 2010 and things have changed a bit, especially in the realm of loans and paying for your education.
I think having a degree is valuable, not just for stage management, but for other employment. You may decide you want to do something else with your life down the line, or you might need to support yourself with a day job while getting your SM career off the ground. Not having a degree can hold you back. If you have a degree and another candidate doesn't, having the degree gives you a leg up. That being said, I don't think it's necessarily required to have a degree to SM, and college is not the right choice for everyone.
One of the best things I got out of my education was the connections- I can directly trace subsequent employment to relationships with the professors and artists that I worked with there. College can give you a "safe" place to fail, and the opportunity to add a bunch of credits to your resume. It also gives you the chance to get a well-rounded theatrical education- having some knowledge of lighting, sound, costumes, etc can help you become a better stage manager.
If you do decide to go to college, there are ways to make it more affordable. Going to community college for 2 years and then finishing at a 4-year school is one option. I don't think putting yourself into a mountain of debt is a great thing, for what is not an especially high-paying career (for the most part). You can also get a degree in something other than theatre, and still work/take classes in the theatre department. You can also apply for need-based or merit-based aid.
I am a huge proponent of internships and apprenticeships- they are a great way to gain experience and build up your resume, as well as build relationships with different theatres. Personally, I don't think that workshops are much of an indication of your skills and experience.
I guess that it really depends what you want to do- I think if you are interested in working at larger professional houses, most SMs there have degrees, in my experience. If you don't have a degree, you need to find a way to boost your experience to stay competitive.