Well, let's see.
UT Austin's degree requirements are https://www.cs.utexas.edu/sites/default/files/images/BS%20Ch... and course descriptions are https://catalog.utexas.edu/general-information/coursesatoz/c...
That's about 16 required classes including Linear Alg., Statistics, A Child's First Programming Class, Data Structures, Discrete Math, Algorithms, Architecture, Operating Systems, plus another 8 of your own favorite upper division electives (CS 340 and above).#,##
Then there's the question of what you mean by "studying". Just reading the books isn't really going to work. That's 50 semester hours---weekly class wall-clock time---and the ol' rule of thumb was 3 hours studying per hour of class time###, for 15 weeks or 3000 hours. But you might be able to do it in less.
So, it's doable, certainly.
A formal degree program has two advantages:
1. Having somebody to advise you on what's important and what's not. Not all of the chapters of SICP are equally meaningful, and having someone who already knows this shit and can say, "pay attention to this chapter, it's important," or "skip those exercises, they're not worth it," or even "forget that section, it's outdated; here's a paper" is quite useful.
2. Feedback. Even if you have the answers to the exercises, having someone to look at your crappy program or broken proof#### and tell you "you are missing this, try that instead" will speed up understanding considerably.
And that's aside from answering questions and making a second pass through some material when you're sitting there staring like you've been hit with a captive bolt gun. It's significantly more efficient to get to understanding than working on it yourself.
And then there's the requirements for things that you would not, yourself, choose: Spanish? !@$&%){ Calculus? Those damn writing requirements? Ethics and leadership? You touch on this yourself: many of the self-taught people I've seen have been depth heavy with little breadth.
Which brings me to another point. Those computer people who built the internet typically already had degrees in physics, math, EE, or something else. And, they also tend to have that depth to breadth problem. (Then there was the afternoon I spent explaining to a former Aerospace Engineer (and quite good programmer) why string = string + character was so slow. And why it wasn't slow on that other implementation.)
# This has actually been dumbed down since I went through in 1986-1990; it used to also include a full class on formal logic, automata theory, and basic electronics. So, hmph. But then I didn't take physics, chemistry, or biology, so yay.
## Stay away from CS 340. It sounds like fun, but it seems to be taught by Warren Hunt...
### Hahahahaha, wheeze... Ah, weekend nights in the computer lab...
#### They're the same thing, remember? :-)*