The National Network of State Teachers of the Year has released a report on teaching emotional intelligence.
Overall, they find research in this field persuasive. That is, these award-winning teachers think it likely that social/emotional intelligence can be taught, and does benefit students in a number of ways.
At the same time–and for obvious reasons–they think more professional development and more funding are important. And, they worry about including these measures in teacher evaluations.
If your school is considering these questions, this report might be a helpful place to start.