I've had the extraordinary privilege of working with all kinds of people; PhD's and high school dropouts, theoreticians and mechanics. I had a friend who "felt" advanced math the way the rest of us feel music. I knew a Boatswain's Mate who quit school in the 10th grade, but could take some wood and rope and hoist you and the horse you rode in on up to the highest rooftop, pretty as you please. They were both geniuses.
Nonetheless, neither was socially awkward. I have met people of every stripe that fit that description. I think we construct the stereotype of the geniuses who can't dress themselves properly and the blue-collar worker who deep down is thick as a brick so that we may better deal with the uncomfortable fact that some people, no matter their education or social status, are simply exceptional.
Maybe we're just trying to compensate for our evolutionary aversion to the Gaussian distribution. Some few people are really smart; some few people are really good-looking, or talented or athletic or preternaturally charming or ..., you name it. Some very very few are all of these things.
Ay, there's the rub. These very very few can be seen as more alien and threatening than any extraterrestrial. How do we humanize them? Flaws! If we cannot find a flaw we'll invent one. We can do it for a whole class. Nerds! Geeks! Ha-Ha, you're smart but you can't get laid!
But I'm preaching to the choir! You're posting on this site. You're probably one of the very few (if not one of the very very few). You've no doubt been told that you don't look (sound; dress; dance; whatever) like a

engineer (scientist; physicist; chemist; Boatswain's Mate; whatever).
So; No! Stereotypical nerds and geeks do not exist. They don't exist anymore than Prince Charming or Sleeping Beauty. Or for that matter Sleeping Prince or Charming Beauty.
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