Welcome to the Camera Labs forum.
Unfortunately I have neither the Easyshare Printer Dock Series 3 or a D40 but I note that, in relation to the Easyshare dock, the Kodak site
states "You can also print directly from any digital camera with PictBridge capability, or from most popular memory cards when using the optional KODAK 8-in-1 Card Reader or KODAK 6-in-1 Card Reader
". The Nikon D40 is PictBridge compatible.
So it looks as though you can print but obviously other capabilities like battery charging wouldn't apply. Are there any forum members reading this who have this dock and use it with a non-Kodak camera?