Can the 2013 13" Macbook Air drive an external 4k monitor?
No, it won't support it. The Thunderbolt 1 controller in the Air only supports DisplayPort 1.1 and you need DisplayPort 1.2 to get 4K support, as you mention in your question.

Check out http://www.anandtech.com/show/7049/intel-thunderbolt-2-everything-you-need-to-know and http://en.wikipedia.org/wiki/Thunderbolt_(interface)#Thunderbolt_2