Well... let's do some math, because I'm not too sure without seeing it first hand.
The 2012's and later support up to two Thunderbolt displays (
source). The resolution of one TBD is 2560x1440. So two of them would mean 7,372,800 pixels.
4k display resolutions vary, but let's go with Digital Cinema Initiative's of 4096x2160. That's 8,847,360 pixels.
The numbers are close (17% difference), but the MacBook Air (definitely the 2013's, at least) should be able to support 4k resolutions just fine!
However! I'm not sure off the top of my head if the current Thunderbolt chip in the 2013 MacBook Air's support 4k output. That might be a Thunderbolt 2.0 (a.k.a. DisplayPort 1.2) feature =\
EDIT: Fixed some math because I'm dumb