The Espressif datasheet lists the input voltage as 2.5v to 3.6v.
Can the mod-wifi-esp8266-dev tolerate this voltage range?
I am contemplating powering one with an LS145000 which is an AA 3.6v sized battery.
I wasn't able to find a voltage range for the mod-wifi-esp8266-dev.
Looks OK - mainly because the SPI flash can cope with 4V
In case you use UEXT / other external device you must check those.