Is it possible to execute a binary from LittleFS on ESP8266?

I do not see why that cannot be accomplished. I have never done it with this processor. It would be best if you studied the OTA (Over The Air) programing code so you understand how this works. In other systems we called it an overlay where sections of code would be loaded into RAM then executed. Take a look at this link: ESP_EEPROM is data persistent when flashing new rev or new program? - #4 by gilshultz