Can emotional intelligence be taught?

I just saw a news clip on emotional intelligence being taught at schools. They claim that children who are emotionally well connected do better in school and are better leaders and also behave better. I’ve known intelligent children who were great in school and grew to be excellent leaders despite having awkward social skills and behaved well in school.
I can see where social skills help, but I’ve also known children with excellent social skills who do poorly in school and who grew to be followers instead of leaders and in some cases also behaved poorly.
1.Do you think this is hogwash, or is this possibly true.
2. Can emotional intelligence be taught if you lack the skill, or do you need to be born with the skill?