Does the LTC4412 part protect against reverse voltage in connecting the wall adapter and battery.
The external PFET will not conduct if the battery is reversed, nor will external diode if the wall adapter input is reversed.
LTC4412 should survive and current will be blocked if:
The reversed voltages are under 14V (abs max of VIN and SENSE)
|BVDSS of PFET| > Wall adapter + battery voltage
|Breakdown of diode| > Wall adapter + battery voltage