If, instead of using the metric getting a job as a Software Engineer, you used building and deploying quality software in a timely and cost-effective manner, then a CS and/or SE degree may be very important.
When I worked in IT, I noticed a correlation between the absence of each. Those who get jobs as programmers without prior study and/or training tend to be more likely to slip up on quality delivered, deadlines met, and/or resources used. Of course, measuring those things is tricky. Some programmers ship software full of bugs so they can make more money fixing it up later, which is charged to some other account in the company.
I've yet to see a correlation between the two.