I have I BFA in fine art and I do think that it dose help as far as telling potential employers that:
1) Committed to learning
2) Teachable
3) Sometime helps getting you the door or at least not the trash bin right away=)
School helped me because most of my work is modeling based right now the way I have been trained to see helps so much. Being able to break down ojbects into lines and form in my head even before I start to model is invaluable to me. All this can be done on ones own but it comes faster with the right teachers.
Yes It's is a peice of paper but it dose show that you have worked hard to learn a trade. I know that with out school it would have taken me quite a bit longer to get to the point I am now. Not to mention I cant read or wright very well because im dislecsic. Which would have slowed me down even more trying to read books because at the time there was not a lot of video tuts avialable.
School I think is just a faster why to get the tools and skill sets you need to improve at a faster pace instead of trying to learn on you own with books or a few tuts here and their. Most people learn from watching rather then reading at a faster pace.
It comes down to the person. If you feel that you can learn the programs on your own then that's awesome, but if you think you would like a bit of help and be able to see it hands on then school is great.
Just my 2 cents.
I am enough of an artist to draw freely upon my imagination, knowledge is limited, imagination encircles the world. (Albert Einstein)
https://www.artstation.com/kurtb