No, that won’t work. Just that they use a similar frequency does not mean they are interoperable! A ESP8266 is a WiFi chip, not Zigbee. Both are also completely different in their protocol. There is, for example the TI CC2652, which is something equal but for Zigbee. It is used in Sonoff ZBMINI, for example.
WiFi is also not suitable for battery powered devices, because it draws too much power. Zigbee is much bettwr for this. I head the same issue and reverse engineered such a sonoff switch. It can be powered by 3.3 or 5V by simply bypassing the internal powersupply. Using the internal transistor instead of the relay is good to drive small lights, maybe add a mosfet for more power.