I have personally had some significant issues getting myself to deal with problems in a constructive way--I was diagnosed with depression several months ago.

I put off seeking treatment, and especially medication, for essentially irrational reasons.

More recently I have started taking Lexapro, and I am MUCH happier. A large part of being able to make that decision came from Less Wrong--the ideas of "happiness set points," beating procrastination, and the idea that using technology to help improve myself is natural and necessary, helped me close the gap between not doing anything and doing something effective.

There are plenty of stories going around about people using decision theory to lose weight.

I would say there are several examples of people who have used the methods of rationality (or at least have used Less Wrong) to help with uncommon problems.

Unless your friend is intensely theist or overly sensitive to contrarianism I can't think of what downside there is to this experiment.