The answer to your question is a qualified yes. In mathematics and in the physical sciences, 90% of what you learn is through self-study. Ideally the professor is there mainly to help you over the difficult parts, so that you don't waste a lot of time spinning your wheels.
The part about self-struggle is essential though, if you want to achieve real mastery of the subject matter, and to make significant contributions in your field. After you finish your post-graduate studies, the professor will not be available to hold your hand.
There are some people who get their advanced degrees on the strength of superior memory and excellent pattern recognition skills. There are a lot of hacks who memorize magic formulas, with precious little understanding the of their essence. And they never make the big discoveries.
Outside the physical sciences, self-study is a different ball of wax. Trying to get a professional job, without the piece of paper can be very difficult. However there's always room at the top, as the old saying goes. If you can demonstrate your extraordinary abilities, and the knowledge that you've gained through self-study, you may be able to create a job for yourself.
The book, What Color is Your Parachute, will probably give you a better perspective.