It should still charge whilst turned on and connected to either mains/PC or external battery pack.
When turned on and connecting to ext. bat. pack it turns on the backlight and pops up a very small window with no readable text. Pressing menu shows the battery charging icon, a battery with a lightning bolt image. Disconnecting when turned on it displays a message, press enter to clear it and continue.
With the device turned off connecting to ext. bat. pack turns it on. Turn it off and it displays the charging icon. Try to turn it on and the charge icon is replaced with the PC connected icon.
AFAIK the differences between the charging cable and the data cable is the data wires, tx/rx, are not connected in the power one.
605 with the 3.10 firmware.