If not, why not?
Because if the two groups are doing the same things, what is it that you're testing?
Actually, now that I think about it, I don't understand why you think the two groups would be doing the same thing, even given your assumption that PUA is an accurate model. If PUA is accurate, then the people in the PUA trained group would end up behaving more like naturally socially successful people, and the control group would go on being geeky (or average, or whatever you select the groups to initially be), and hence the two groups' results would diverge.
Maybe you need to re-read the experimental protocol I suggested.
Followup to: Do you have High-Functioning Asperger's Syndrome?
LW reader Madbadger uses the metaphor of a GPU and a CPU in a desktop system to think about people with Asperger's Syndrome: general intelligence is like a CPU, being universal but only mediocre at any particular task, whereas the "social coprocessor" brainware in a Neurotypical brain is like a GPU: highly specialized but great at what it does. Neurotypical people are like computers with measly Pentium IV processors, but expensive Radeon HD 4890 GPUs. A High-functioning AS person is an Intel Core i7 Extreme Edition - with on-board graphics!
This analogy also covers the spectrum view of social/empathic abilities, you can think about having a weaker social coprocessor than average if you have some of the tendencies of AS but not others. You can even think of your score on the AQ Test as being like the Tom's Hardware Rating of your Coprocessor. (Lower numbers are better!).
If you lack that powerful social coprocessor, what can you do? Well, you'll have to run your social interactions "in software", i.e. explicitly reason through the complex human social game that most people play without ever really understanding. There are several tricks that a High-functioning AS person can use in this situation: