No, it does not. Learning new skill from scratch takes time. You're trying to master 2 new, orthogonal, in some sense contradictory skills: web development, and self-promotion (to find your place in "the job market"). Take a deep breath.
There's a difference, and not insignificant, between "learning everything for CS degree" vs "learning what you need to get hired as a web dev".
But I'll agree that 6 months is not that much time in the "learn new career skills and find a job" timeline. I spent around 18 months of nights/weekend practice and learning, followed by 3 months of interview prep before I found a job and that was with a big spoonful of luck.
To OP - this is a marathon, not a sprint. Get used to learning things on your own, you will be doing it for the rest of your career if you make the switch.
Cannot second this enough. As a developer, there will always be new tools and technology. More room to grow into adjacent development. And more line of business knowledge to gain. I can't think of any other field, that has more lifetime learning involved in it.
Which isn't to say the non-programming stuff in my degree was irrelevant, but you don't need to spend 4 years full time studying to learn relevant skills for a junior web developer job, and you could easily learn them in less time outside of a degree.
Granted, he's very smart and basically coded all day for 6 months, but I'd say it is possible for a motivated individual.