From my experience, a strong CS background is the difference between software engineer and a prolific coder. With equal experience, the engineer’s results tend to be better optimized and easier to maintain. Of course there are exceptions to the rule; a naturally gifted coder can overcome some of these limitations by using patterns and algorithms that he’s learned from experience. Without the math, you’re limiting you potential and going to spend a lifetime reinventing the wheel.
Honestly, I've had mixed experiences. I've worked with both great CS students that failed in real-world efforts and poor to mediocre CS students that excelled in real-world efforts. I've also worked with professional developers with no official CS training that were some of the best engineers I've ever worked with (one had a philosophy degree and another a physics degree).
I think there are 2 fundamental indications of indication of success in software development/engineering: 1. an eagerness and desire for continued learning. 2. passion for the quality of the product. Sure, there may be other factors, but I think if you don't have these 2, they're probably not going to be a positive net contribution on a project.
