There is a problem with the logic in this theory in the sense that employers (especially the larger ones) don't have time to go and investigate every class you have ever taken to verify the content to make sure it is relevant to what you are hoping to do for a career. Sure everyone knows about and has heard of Harvard, University of Texas, Michigan State, Arizona State, et. al. And if a potential employee shows up with one of those well known schools on their resume, we as hiring employers are going to assume that the quality of education was at the very least, on par with most other schools that are accredited by the same agency.
If you go to a lesser known school (online or otherwise) that is still accredited, it may be important to mention that the school is in fact accredited. That doesn't guarantee that you learned anything, but it does give the employer some level of satisfaction that you were offered rigorous courses that had some meat to them.
On the other hand, if you spend your money at a school that is not accredited, yet still offers degrees, you will remove that comfort level from the employer, and probably even have to explain your entire college career to them since they are not familiar with the school, and more importantly, have no idea about the curriculum. While distance ed is still in it's infancy, and is growing by leaps and bounds, there is still that legacy relationship between accreditation and quality.
Just my opinion: If you (or anyone) is going to spend a bunch of money on getting a degree from any school, it might as well be accredited by an agency that everyone recognizes and accepts. It can only add value to your degree and your overall education. As someone who hires about 30-50 people a year, I can tell you from experience that if two people with absolutely equal talents, skills, ability, etc... came into my office, and one had a degree that was accredited from a regional agency, and the other had an unaccredited degree, the accredited one wins all day long. In the long term, I am just afraid that you will regret your decision and the amount of money you spent on it. Knowing that for the same price or a little more, you could have done better.
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Scott
http://www.WheelCipher.net