I didn't see anyone say this, but one of the things I have figured out is that you must plug it straight into the wall via the USB power plug that comes with your iPad. The iPad doesn't seem to like the low voltage from the computers USB ports or even powered USB hubs.
With that said, yes it will charge while it is sleeping on the dock and saying it is not charging. However, if you want it to charge while using it, you have to plug it into the wall. It's stupid, but it is the world we live in. It is the only way to deliver enough power to sustain what you are doing with the screen on, and still have enough power to increase the charge. Even doing this, in some instances, will not actually charge the iPad due to using wifi, bluetooth, etc. If you just want a quick charge experience, plug it into the wall, and leave it to go to sleep. It will then charge at its full potential and speed.
-Cheers!