Does the battery module charge the camera while connected? Or does it only provide power?

It charges.  

Hello there nomnomnom. Good day and thank you for the inquiry. Kindly please refer to the post above and in addition, the DJI Action 2 Power Module increases the DJI Action 2's battery life, includes a built-in microSD card slot, and can be used with an external microphone. With the magnetic lock, this hot-swappable module can be attached to the Camera Unit, allowing you to get more out of your DJI Action 2. When connected, your DJI Action 2 can film for up to 180 minutes, so you can fully enjoy recording without missing a beat. Thank you.