I tested this personally, and the most correct answer is: They charge up to about 50% and then stop.
I let the JoyCons completely discharge until they would no longer function, then attached them to the console in handheld mode. As you can see in this picture, the JoyCons are indeed marked as charging. Ultimately, they got up to each half full, but there is no way to tell the exact percentage with the current GUI.
My best guess is that the Joycon batteries are simply wired in parallel with the main battery so they charge up to, but never exceed, the voltage of the main system battery because the system does not boost the voltage to charge them which is why Nintendo doesn't list this as an official charging method.
If your PS3 controller has been unplugged and out of battery for a while, it wouldn't be able to maintain it's 'sync' with your PS3.
You will need to attach a USB cable to the PS3 and the other end to the controller for them to sync up properly again.
The other side of this, it's that the batteries in the PS3 controller have potentially degraded to the point where they will no longer hold a charge. If you leave them charging, but they switch off immediately once being unplugged, this is likely the case.
You should still be able to play games with them so long as they are plugged in to the PS3, but long term it might be worth investing in a new controller.
The Pro Controller can be used whether the Switch is docked or undocked and regardless of Mode. It can be used either when the Nintendo Switch is docked at home and connected to a television in TV Mode or when the Nintendo Switch screen is undocked in Tabletop Mode, allowing the screen to become a portable television screen for the Pro Controller to be used with.
Best Answer
I tested this personally, and the most correct answer is: They charge up to about 50% and then stop.
I let the JoyCons completely discharge until they would no longer function, then attached them to the console in handheld mode. As you can see in this picture, the JoyCons are indeed marked as charging. Ultimately, they got up to each half full, but there is no way to tell the exact percentage with the current GUI.
My best guess is that the Joycon batteries are simply wired in parallel with the main battery so they charge up to, but never exceed, the voltage of the main system battery because the system does not boost the voltage to charge them which is why Nintendo doesn't list this as an official charging method.