I don’t have any breakdown on the numbers, but it seems to me that if introversion is more about lack of desire to socialize and AS is more about inability to socialize, they don’t necessarily need to be correlated, although they may very well be.
Wikipedia quotes diagnostic criteria for AS that focus on 'impairment' and 'repetitive, stereotyped behavior,' which sounds like it's just based on ability, not desire/introversion. That's consistent with your hunch.
I also skimmed for studies correlating AQ (Autism-Spectrum Quotient) with introversion, and discovered the AQ is built from 5 question types, one of them testing social skills. But the social skill questions don't just test for ability (#36, 'I find it easy to work out what someone is thinking or feeling just by looking at their face'), they test for desires too (#1, 'I prefer to do things with others rather than on my own'). (Source is Simon Baron-Cohen's paper about the AQ.) So I'd expect the social skill subtest to tap into introversion as well as social ability, which would make the AQ correlate with extroversion/introversion (and it does).
I expect the correlation of AS with introversion depends how you measure Asperger-ness. The binary criterion 'diagnosed with Asperger's' probably has a weak correlation; the AQ scale would have a better one. It's interesting that AS diagnosis criteria are based just on social ability, while the AQ scale tests far more than that - that suggests the AQ is measuring quite a lot more than Asperger-ness.
(I also found a forum called Typology Central, 'a personality type indicator community.' For some reason the idea of a forum for discussing personality types makes me giggle.)
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: