Does the Nintendo Switch charge the JoyCons in Handheld mode while undocked and unplugged?
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.