I think that companies and organizations willing to participate in some form of a casual Friday does help to boost morale, which will then boost productivity. It's just nice once a week to be able to wear jeans or something to that effect. I wish my company allowed us to do that.
Casual Fridays are a great idea. Reason being? Most people work better when they are in a comfortable, relaxed environment. A lot of folks confuse being casual with being unprofessional, but this isn't at all the case. You can still be relaxed, dressed casually, and very productive. And have fun while you're doing it.
Yes, I do think that having a casual Friday will give people a change in the regular work routine, and make them have a day where they feel more relaxed and comfortable, and make being at work more enjoyable. These things will cause them to work harder and increase productivity.
I do not believe casual Friday's increase worker productivity. Most Americans do not live in situations where a casual Friday exists because they are stuck in low-wage jobs that require daily uniforms or dress codes that are not changed. For those taking advantage of casual Friday's they are probably accustomed to putting in less than their best on a daily basis anyway. I believe companies foster this problem by allowing employees too much free time. This won't be helped by implementing a different dress code on day a week because you're simply giving the employee more freedom.
Casual Fridays do not increase productivity. I do believe that it helps with worker satisfaction and happiness at work. I believe it is the same as telecommuting. It alleviates some pressure but it certainly does not increase productivity just because an employee is more comfortable in casual clothes or more comfortable working from home.