All device manufacturers advise against doing firmware update when your device is connected via WiFi. A wired connection is advised.
I am not sure what happens if you lose your wifi connection halfway through the firmware update of your drink camera. For one of my Linksys routers, it bricked the router beyond repair. I had to throw it away.
Having said that, I have managed to do firmware update of my cameras using both wired and wifi connection. I did note that the process was slower when doing via wifi connection. I took a calculated risk, as the camera was mounted up on the ceiling and I was too lazy to take it down or pull a cable up. You have to decide whether you want to take the risk.