No, the body diodes do not pass any current when the MOSFETS are off.
You need to draw a flowchart to see how the circuit operates.
Step 1. Is a positive voltage (w.r.t. ground) available on EXT_P5V0?
If Yes, then: Q100 turns on; Q102 turns on; Q101 turns on; EXT_P5V0 goes to U101./EN, which will disable U101 if it is a logic high (~>2.5V). Stop.
If No, then: Q100 turns off; Q102 turns off; Q101 turns off; R107 pulls U101./EN down to ground, which activates U101. Go to step 2.
Step 2. Is VCC_EDBG_USB_P5V0 above the threshold of U101.VSNS?
If Yes, then U101.IN1 opens and passes to U101.OUT. Stop.
If No, then U101.IN2 opens and passes to U101.OUT. Stop.
For extra credit, describe what happens if EXT_P5V0 is between 0 and 2.5V.