I don't think so. Many short guys seem to be doing just fine. Look at celebs like Tom Cruise, Taylor Launter or Zac Effron. They're heartthrobs. Sure a tall guy is striking but if you don't have the personality for it. Its just a waste. I'm 6'1. I wouldn't call myself short, but I have friends who are sort of short but way ahead of me in the dating pool.
They do which is sad because no one has any control over their height yet because of this standard a lot of guys are either proud/arrogant or humiliated and embarrassed over something they have 0 control over.