Do AirPods charge batteries with Qi now?
Yes, but... 

Current AirPods can only be charged with a Qi-compliant charging pad if they're in the appropriate case. By appropriate case I mean Apple has launched a new optional charging case that supports wireless charging for AirPods.

[EDIT]

You may wish to read:


Apple announces a wireless charging case for the AirPods
Apple Intros AirPower Charging Mat, Wireless Charging AirPods Case



  Apple revealed a new AirPods case that works with Apple's new AirPower charging pad. To charge the new wireless case, you place it
  on the AirPower. If your AirPods are in the case, you’ll see an orange
  light if they’re charging, or a green light when they’re nearly fully
  charged. If no AirPods are in the case, the light still goes on when
  you open the lid, but it indicates how much battery life is left in
  the case itself: orange for needs charging and green for good life
  left.
  
  As of this writing, Apple has not released pricing for the new
  wireless case, nor has the company said that it will replace the
  original case with the new one with a new pair of AirPods. The
  wireless case will be available in 2018.


Source: See second link above