That depends on why you are attending seminary. If you wish to have a degree that will be recognized for what it is, then by all means attend seminary and at that, an accredited institution. If you are just trying to gain an education, there are other ways to do so, though the rigors of the academy are such that people tend to learn more, study harder, and study broader in any given topic than if left to their own devices (for the most part).
In my own Bible college and seminary degree work, I did all the class requirements, wrote all the papers, did all the various assignments, and wrote all the quizzes and tests. I was able to participate in classroom discussions where topics akin to what we find on this board were discussed on a regular basis. I was able to hang around with the men who wrote the books that everyone else studies. At the end of the day, it was quite a blessing and I am deeply grateful to our glorious God for gracing me in this fashion.
During my two degrees, I read an average of 3 books per course (with some requiring upward of 10 per semester. I averaged 3-4 classes per semester, so I read 9-12 or more books as required reading per semester. That comes out to about one a week or so. That is a pace that few self-study students will hold. On top of that, I spent 3 semesters each in Greek and Hebrew studies, which required huge amounts of memorization. I would typically spend 2-4 hours each day working on language memory. That is on top of the books required. Then, there were always papers due. Short papers like 5 pages were no big deal, but even they took a week or so to process because they typically require at least 5 source materials, from which accurate footnotes were required. 15+ page papers often required dozens of books, journals, etc., and took several weeks each to prepare, and no one professor ever really cared that another had his coursework due on the same day. So, at the end of the day, earning a degree from an accredited seminary takes pure and plain WORK.
But, here is the interesting point. Along the way, I also read work that interested me. During my Christian life, I've done an extensive study of biblical and scientific apologetics, work in marriage (including counseling), church planting and missions, and work in theological history. With those four additional topics added to my course work, I added about 3 books per week to my reading list during times when I was not swamped with school work. At this point in time, I've read and processed somewhere in the neighborhood of 1000+ books on theology and church related subjects. I have "self studied" along side my academic career to a very high level.
I also started a consulting business, where I edit and format doctoral dissertations for seminary students. I work with students on 3 campuses and at a very high doctoral level, which further exposes me to theological thought, some cutting edge and brilliant, some horrible and a waste of time and paper, and from my long and fruitful studies, I know the difference. In fact, I can often tell whether a person mis-quotes a source material in his work (or worse, plagiarized) because I've worked through that work myself.
In conclusion, you can study hard and do it at home if a terminal degree that is recognized by others is not important, but I've found that the degree, even performed poorly is worth tons more than all the actual study in the world. Best of both worlds is to study to show oneself approved, and to get the degree to go with it -- my course of action.