If we’re talking about doing “wifi” (rather than your “wife”) then the answer is, “Yes”. The ESP8266 has an analog input pin. 
As @Toro_Blanco suggested, you should be using an ESP8266 development board (e.g., Wemos D1 Mini, NodeMCU 1.0 / ESP-12E, …), rather than a ESP8266 “chip”.
With some projects (not yours), the ESP8266 may not provide enough GPIO. I assume (not sure) folks are using the Uno for increased GPIO and the ESP8266 simply for wi-fi connectivity. There’s always the wifi- and bluetooth-enabled ESP32 which has more GPIO. In this day and age, an Uno certainly wouldn’t be my first choice.
By the way, there are a few ESP8266- and ESP32-based developments boards with onboard lithium battery charging circuits (i.e., you can directly connect a lithium rechargeable battery). This may be of benefit with your application.