That is correct:
https://arduino-esp8266.readthedocs.io/en/3.0.2/ota_updates/readme.html
the first firmware upload has to be done over a serial port. If the OTA routines are correctly implemented in the sketch, then all subsequent uploads may be done over the air.
The esp8266 boards platform comes with a library named "ArduinoOTA". You must upload a sketch to your Arduino that uses the ArduinoOTA library to watch for an OTA upload and write the incoming data to the ESP8266 board's flash memory. You will also need to make sure that every sketch you upload over OTA after that has the ArduinoOTA code, since if you upload a sketch without that code, or with the code not working correctly, you will not be able to upload again over OTA and you'll need to once more upload a good sketch over the USB cable.
Check the link above for lots of good information about OTA.
There might be some special considerations for ArduinoDroid. I don't have any experience with that application so I can't advise on that. However, I see that there are multiple options for OTA uploads, only one of which depends on the Arduino IDE, so it does look promising.