Charging the Puck.js wirelessly with QI wireless charger

You couldn't do it without some modifications I'm afraid - as @allObjects says there isn't the hardware in the chip to handle wireless charging.

I wouldn't suggest it I'm afraid - there are a few things you'd need to look out for:

• LI2032 batteries can be at 4.2v when being charged, but Puck.js maxes out at 3.6v - so you'd need a voltage regulator (or a diode to drop the voltage).
  
• I'm not sure how the existing NFC coil would cope with the power being sent to the separate coil - it'd definitely pick some of it up, and it could damage the nRF52 module
  
• Physically you might have trouble fitting the charger board into the existing casing
  
  

You could potentially cut the NFC tracks that lead to the nRF52 module, then add a full bridge rectifier to the existing coil - along with a diode to drop the voltage from the battery - but it's turning into a pretty serious modification.

I should have a small Bluetooth LE board available soon (rather than the cased Puck.js), and it'd probably make more sense to try something with that instead?