Charging Lipo under load
Adding a load to the battery while charging means that the load is actually added to the charger. Since the charger must provide enough current to both charge the battery and supply the device there may be issues if the load is disconnected while the battery is being charged.

Microchip's AN1149 describes a method for converting a battery and charger into an offline supply that switches to wall power when the battery is being charged. Since the charger only ever has the battery as a load, the above problem is avoided.