When my KT runs out of power while I'm reading, the screen just goes blank. If I then plug it in to charge, I get a black screen. At that point I usually power it on, then put it into Sleep mode, and it continues to charge while showing the battery meter icon on the screen so I can monitor it.
If I want to keep reading while charging, I can - no problem. In fact I have a small portable USB charger/spare-battery that I carry in my bag. If I run out of power on the go I just plug the KT into that and keep on reading. I can still hold it in one hand, holding the portable charger against the back of the KT with the USB cable hanging below. Cost me $10 at a local store (sort of like this one:
http://www.dealextreme.com/p/2200mah...le-black-44914)
Some people have mentioned that the KT will display a low battery warning message telling you to recharge, but apparently it only appears if the unit was in Sleep mode when it ran low on power. If my KT runs out of power while it's off, it just won't turn on again (the blue LED on top next to the power slider flashes on briefly, then nothing).