If the schematic found here is correct, then that’s impossible. The ESP8266’s “EXT_RSTB” signal couples via a diode (D3) into “RESET” which is also the Mega2560’s reset signal. You would have to find and desolder D3 to make this work.
You should be able to find the D3 diode with a multimeter since it would be directly connected to the RESET pin (on the header) on one side, the other side going to the the ESP8266.