A pair of headphones has space for something the size of a Fiio E5 (potentially several times that size), but there's no way Apple or anybody else is going to built that quality internal to a phone.

Earbuds won't have the space for that hardware, so I expect the phone will still have an onboard DAC and an analog output mode over the lightning connector for use with cheap/small lightning earbuds and to allow a passive lightning/3.5mm adapter.

EDIT: As an addendum, I'm expecting we'll see a lot of bluetooth headphones with the iPhone 7, following in the Apple Pencil's "plug into lightning to pair and charge" setup. Hopefully also using the wire for data while they're connected.

I think that's the point of lightning - they can derive power through the port. As for size I think there's already a few products out there that manage it. I saw one reviewed a few weeks ago.