Charge battery of NX200 via USB?

This is a nonsense answer. Haven't you heard about voltage transformers? For AC it's obvious this happens everywhere in your house, but for DC it's also possible. You can get any voltage you want from any other voltage.

So the issue is only this: Does the NX200 have a USB battery charging circuit in the camera? I don't know, but if  it doesn't work with the included USB data cable, then probably not...