The description for alternative boost converter without disconnect is preserved below just in case someone might want to hack a $0.50 USB voltage booster instead.
At power off, the /SHDN pin is pull down to 0V via resistors R17, R16 and R6. This put the boost converter in shutdown mode and should be drawing less than 1uA of current.
There is a conductive path from the battery through the inductor L1 and the diode D1. P-MOSFET is there to isolate the rest of the circuits. Transistor Q1 is off as its base is at 0V. P-MOSFET is off as R12 forces its VGS to 0V.
When the push button S1 is pressed, the /SHDN pin is raised to the battery voltage. This enables the boost converter. Transistor Q1 is turned on pulling the gate voltage of P-MOSFET to ground. VGS of Q2 is now at -5V. It conducts and connects the output of the 5V supply to rest of the circuit.
There is a conductive path from the ADC input ESD protection diode(s) to the VCC rail. Q3 is used to isolate the battery supply voltage from the ADC input when the microcontroller s supposed to b powered down. Gate of Q3 is connected to the VCC and when it is raised above the VGS threshold of the battery voltage, it turns on connecting the ADC input.
At some point, the microcontroller wakes up and set PD6 to a logic '1' to latches the power on. The microcontroller can power itself off by setting PD6 to logic '0'. R1 is there to protect and override PD6 when S1 is pressed while the microcontroller tries to power down by setting PD6 to '0'.
PD6 is pulled up to 5V by R4 and R17, but dropped down towards the battery voltage (1.5V or below) when button is pressed.
I sketched out the circuit in LTSpice to calculate the actual voltage as circuit is non-linear. Q1 should turn on at around 0.746V which matches the minimum startup voltage of the MCP1640.
PD6 is at 1.1V when battery is at 1.5V. This is within the logic level '0' from the datasheet.
Low '0' VIL(max) = 0.3*Vcc = 1.5V (for Vcc = 5V)
For a typical part (i.e. not guaranteed), the threshold is around 2.25V. You can probably get away with R17 = 0R.
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