I forgot to mention one thing: The above circuit has manual switch (SW1) to disconnect the load from the battery, I'm assuming it is used to do so during charging. I don't know how exactly will LiPo cells behave when being charged under load (the switch accidentally left on), but in all likelihood it is not good idea - most charging circuits I've seen contain a switching element (i.e. MOSFET, either built-in or external), which automatically disconnects the load from batteries and connects it to the external power supply, and vice-versa (automatically connects the batteries when external power supply is detached).
the original circuit had the same switch and it was supposed to be working while charging (even had an extra animation, thats what the charging detection circuit is for). From what i read about lipo batteries it is possible to power a circuit while charging.