Yes, it will – if you apply to the right places. :)
At a large company, you’ll often need the CS BS degree to even get your resume past HR and into the hands of a hiring manager. Your side projects may help a little, but often not much, I’ve found – it depends on the hiring manager.
But at smaller companies, like the one I’m the lead developer for, you can easily get hired without a degree, if you’re actually good at programming and working in teams. That’s because we tend to look for qualified people, not necessarily people with credentials. I’ve met many very poor programmers (in real-world terms) with advanced degrees, so I no longer look much at applicants’ education level; instead, I check for lots of personal projects (which indicate a love for programming that pretty much can’t be faked) and past work experience, ask lots of questions in interviews, have applicants write code during the interview, etc. So in that case, your side projects would probably be the thing I’d care about most.
At this point, though, it sounds like you might be a step ahead of yourself; I’d recommend taking some classes, just to see if you’re really as interested in development as you think you are, and to figure out your specialty(ies). You really do need to love programming to be much good at it, i.e. to make money at it. Once you’re sure it’s the field for you, then you’ll be ready to look for places that will be willing to give you your first crack at doing it for money.
Finally, I’d note that even if you find that you don’t like programming enough to pursue a career in it, a light understanding of it combined with a psychology degree will give you excellent credentials for related jobs, like project management.