It would be tricky to support the shields. Arduino is 5V. The BeagleBone is 3.3V. So you would need bidirectional level shifting on all of the digital signals. Analog is only analog on the BeagleBone and limited to 1.8V.
Now, adding an Atmel processor onto the BeagleBone, that is easy and is already being done.
http://ninjablocks.com/open-source/
Gerald