Is it possible to charge a lipo battery connected to a battery shield and a Photon possible?

When your code takes care of that, it is possible.
The WiFi object does provide the required functions for it.

If you add the respective hardware to your project then you can virtuallly do anything - inductive charging would be one of these things.

But exposing USB (or any other set of pins required for your needs - there are multiple ways to do what you want) would be the most logical IMO.