Yes, at least with Apple compatible headphones. I bought the adapter specifically to connect my Bose QuietComfort® 20i Acoustic Noise Cancelling® headphones for Apple® devices to my iPhone 6s through the 6s Smart Battery Case lightning port (because the Bose have a L-shaped connector that won't insert through the straight opening of the battery case).
The 3.5 mm to Lightning adapter allows full pass through of in-line mic and controls. On initial plug in to the Smart Battery case Lightning Port of the 3.5mm to Lightning adapter with the Bose, the controls did not work. However, unplugging and replugging the adapter with the Bose Headphones attached allowed the controls and mic to work.
As long as your headphones are designed to work with iPhones, then they should work with the 3.5 mm to Lightning adapter, at least on a 6s using a Smart Battery case. As I don't have my iPhone 7 yet, I can't speak specifically for the iPhone 7, but it works fine even through the Lightning port on the Smart Battery case with the 6s and the headphones I have tried. Again, sometimes you may need to unplug and replug into the Lightning port.