If I left the battery shield plugged in for extremely long amounts of time, will the shield know to stop charging the LiPo battery or will it overcharge the battery?
You should be fine. The shield will ‘charge’ the battery indefinitely as long as its plugged in that way (although not suggested). The current being delivered for charging will change over time. As the battery is charged up to target levels then the current will lessen. Once the battery meets a certain level of charge the charging LED should turn off.
I was planning to use the battery shield as a sort of backup battery, in case someone accidentally unplugs the USB as the Photon is running. Is there a way I can program it to stop charging and only provide power when the USB isn’t plugged in?
There doesn’t seem to be a direct method with the on board circuitry.