That would be very slow source of random numbers.
I wonder how well it would last over time? Assuming a normal (not precision casino) die, bought off the shelf from a high street store - would you be able to see any pattern in 1 million rolls? Would deformation of the popping base affect randomness at all?
How about a webcam sampling "snow" from an untuned TV?
While Boggle sounds like an interesting method of generating random numbers, I think that a better way would just be to whiten the "random pulse train" output from a Geiger counter next to a weakly radioactive sample and send the resulting numbers over a serial link.
1. a die (D6, D20, etc) enclosed in a clear dome with a base that will pop and cause it to fly into the air and land. The base would ideally be made to pop electronically, maybe by a servo
2. a camera directly overhead the die which feeds into a computing device
3. OCR software that receives the camera input and outputs the number on the die