TPS2116: Bi-directional current flow when the switch is ON.

Part Number: TPS2116

Tool/software:

Hello,

I have the circuit here: https://imgur.com/wxQDq5B  

I have 2 power supplies: "VEE" and "Charging_resistor" which goes to the output as seen in the image. Only one is active at a time with priority is given to VEE.

I need the "Charging_resistor" supply to have bi-directional current flow since it is a battery but I read there is a reverse current block in this device.

output might be 3.3v or 3v while battery can be 3v or 3.1v...etc but still i need it to be charged.

Will this circuit work as intended? 

if not, then i might replace it with back-to-back P-MOSFET load switch and muxing circuit.

thanks