I run a sensor running on a 280mAh LiFePO4 battery. This works fine, ten days without charging/replacement.
As I know, WiFi connection is always stablished, parallel, as ESPBasic starts. When there is a delay of some seconds, the chip has enough time to decide, if WiFi (what takes the most battery current) is needed, or start sleeping again.
Other:
Sometimes it is complicated to integrate a new modules into existing network. When the flasher allows setup via the serial port, life can be easier. At least the WiFi name and password would be highly appreciated. Another solution is the whole Settings command line interpreted right after flashing th firmware.