With nothing connected to GPIO-02 startup is perfect.
I have built projects using ESP8266 outputs for LEDs in the past on GPIO-02 with no problems..
So once my esp8266 starts I can connect the output to GPIO-02 and operates as expected.
This is the project I'm testing: [url]
https://www.instructables.com/id/ESP8266-Internet-Alarm/[/url]