We cross posted. My understanding is that yes you can get extroversion and Aspergers - the result being awkward interactions because they child still can't figure out the social cues any more than if they were introverted.

For what it is worth we are waiting for an ASD assessment for our 9yr old daughter. She's extroverted and makes eye contact and has great empathy, but she only shows that empathy in situations of overt need as she doesn't notice it's needed until there is screaming, crying, blood, etc. A sad face would be unlikely to result in a hug.