I'm not a lawyer, but as a Canadian that does not have a degree in Comp Sci and has been looking for work in the United States since 2006, I'd like to share my experience.

In a nutshell, I've been told time and again that having a degree will help, although how much one that isn't related to your discipline may not be worth much more then the paper it's printed on. To give my experience, I've been told by multiple companies within the last year that it's basically no Comp Sci (or equivalent two year college course), no chance. Your degree in an unrelated field might help a bit, but I wouldn't put much weight in it when it comes to immigration VISA time.