Looks like they're pretty small. They're single chips, and small ones at that. Here's a datasheet for one I found at random:
http://www.ti.com/lit/ds/symlink/pcm1754-q1.pdf
That lists the size as about 6x5x2mm. Should fit comfortably within a lightning connector.
Consider that the new wireless earbuds have a DAC in each earbud, plus a full Bluetooth radio, all squeezed in there.