I think the following two are open questions: Given the same amount of approaches, does a guy who has read PUA theories have higher success of getting laid?
Isn't one of the benefits of PUA is that your number of actual approaches increases (while single, at least)?
Isn't one of the benefits of homeopathy that you get to talk to a person who promises you that you will feel better? If the control for homeopathy is doing nothing that you find that homeopathy works. If you however do a double blind trial you will probably find that homeopathy doesn't work.
If you truly belief in rationalism and don't engage in it to signal status, I see no reason to use another standard for judging whether homeopathy is true than for judging whether PUA works.
A few examples (in approximately increasing order of controversy):
If you proceed anyway...