A circuit like that should work, but the mosfet is oriented backwards. If you will include the body diode of the mosfet in your drawing, you will see why. The body diode must prevent current from flowing from the charging source back through the mosfet to the battery.
But generally it's called a "load sharing" or "power path" circuit. It's needed because the TP5100 terminates charging when charging current at 4.2V or 8.4V drops below 100mA. Any load current could distort the termination process, and might even prevent termination, which you don't want.
