That seems highly implausible, as the MT7688 isn't really designed for battery operated systems.
What you should probably do is use a microcontroller intended for ultra low power / sleep mode / wake on interrupt operation.
Have that occasionally power up the MT7688 (USB power switch, regulator with enable, etc) when it needs wifi. Make sure you either have no persistent file system state, or do an orderly shutdown each time.
Also consider if there may be another wifi solution that is a better fit for your application.