It would give you best useage of your batteries as the input is from 2.7V to 11.8V and it has an enable or shutdown (SHDN) pin.
The text says:
Connections
The step-up/step-down regulator has four connections: shutdown (SHDN), input voltage (VIN), ground (GND), and output voltage (VOUT).
The SHDN pin can be driven low (under 0.4 V) to power down the regulator and put it in a low-power state. The quiescent current in this sleep mode is dominated by the current in the 100k pull-up resistor from SHDN to VIN. With SHDN held low, this resistor will draw 10 µA per volt on VIN (for example, the sleep current with a 5 V input will be 50 µA). The SHDN pin can be driven high (above 1.2 V) to enable the board, or it can be connected to VIN or left disconnected if you want to leave the board permanently enabled.
Lokking at the schematic https://www.pololu.com/picture/view/0J5668
R6 (100k) is just a pull up resistor for SHDN. If you can supply a voltage of more than 1.2V to this pin from your wake up source then the resistor is not needed and could be removed. That inturn would give a sleep current of 0.
This could also handle recharging of the batteries - a solar top up?