Can a replacement iPad screen be used on a BeagleBoard?
I assume you are talking about this touch screen:
http://www.repairsuniverse.com/ipad-2-touch-screen-digitizer-replacement.html

However, without the touch screen controller, it is basically useless. That's because a special controller chip is required to perform the high speed capacitance measurements. 

Take a look at this touch screen from 3M (one of the few capacitive touch screens on digi-key, but there are many more out there)
http://search.digikey.com/us/en/products/17-8031-205/3M5745-ND/1886090

It requires this controller module:
Digikey part No: 3M9138-ND 

I'm willing to bet that controllers are rarely compatible with other touch pannels becuase of the variety of technologies out there.

Also note that Cypress makes a line of capacitive touch screen controllers, called TrueTouch.