My Netatmo Smart Doorbell started making clickety noises as the relay switched on/off in a rapid way. We can still push the button to ding the wall bell inside as the transformer and the circuit itself still works, but taking the Netatmo off the wall it was kind of hot to the touch, probably because it was trying to charge a dead battery.
There is big capacitors on it, so it takes some time before it loses power after being disconnected.
I took the battery out from the casing and mounted it up again without it to see how it works without a battery.
OBS: It seems it does not work, the LED flashes green, and the chimes button no longer triggers the bell inside. It connected and disconnected continuously, so it needs the battery power source to function.
The plan was to source a new battery, but I did not find a suitable one.
In the end I replaced the battery with a 4.2V power source that hopefully will last forever, but it is not a modification for everyone to make. Please do not try to do this if you do not have the experience or the tools. I will not help you with entry level problems and the warranty will be void if you open it.