I think that this is a diagnostic misconception...
A great many individuals with autism are also intellectually disabled.
1 Those with Asperger's syndrome, in contrast, must by definition
have suffered no cognitive delay during their first 3 years of life. 2
This means that they will usually have at least a “normal” IQ.
Basically people on the spectrum with normal to above normal IQ scores tended to be diagnosed/labeled with Asperger's while those with lower IQ's tended to receive other Autism spectrum diagnoses.
Now with that bit out of the way...
The "geek" portion is, as mentioned, fairly obvious:
Asperger syndrome (AS), also known as Asperger's, is a developmental
disorder characterized by significant difficulties in social
interaction and nonverbal communication, along with restricted and
repetitive patterns of behavior and interests. As a milder autism
spectrum disorder (ASD), it differs from other ASDs by relatively
normal language and intelligence. Although not required for
diagnosis, physical clumsiness and unusual use of language are
common. Signs usually begin before two years old and typically
last for a person's entire life.
Ok, so lets break that down:
- significant difficulties in social interaction and nonverbal communication
- This seems pretty classically "geek", probably doesn't require explanation.
- restricted and repetitive patterns of behavior and interests
- I suspect that this is where a lot of the "genius" claims come from. Even someone with an average IQ can become an expert in a field, if it's their only interest.
- relatively normal language and intelligence
- As in not significantly impaired, though it's worth noting the comorbid learning disabilities are not uncommon.
- physical clumsiness and unusual use of language are common
- Probably not an athlete, combined with unusual inflections and voice patterns, further evidence of classic "geek"
As far as a "large scale study" it seems that sources indicate that people on the spectrum are difficult to test and that individual's scores vary wildly from test to test and that testing conditions have a much more significant impact.