I don't see it quite *under* the display, just recessed enough under it that you would be able to see it the keys but it would minimize the space between the keyboard and the display - because reaching OUT and forward is part of the problem. You want the display as close to you as possible, like a book - so you can reach it with your arms bent at the elbows - if that makes sense.
Maybe make the bottom of the bezel on the display clear, so you could see through that part - figure a bezel is going to be an inch or more thick... you could make that less of an obstacle.
Most keyboard trays that slide under the work area are designed to facilitate this kind of thing already, so you can have a book or papers laid out on the workspace, the monitor upright at the back of the desk, and the keyboard is on a tray slight recessed under the workspace. This will probably get me flagged for SPAM, but check out this link:
http://www.amazon.com/Complete-Computer-Workstation-with-Storage/dp/B003FSTNAM/ref=sr_1_5?ie=UTF8&qid=1354756786&sr=8-5&keywords=workstation+deskThose designs work GREAT...
