Nice idea, but a device like this would need power and an Internet connection. And possibly a wireless connection, if you are unable to get it near an Ethernet cable. And of course a custom-designed board, which has development and production costs.

On the software side, it would require at the very least a TCP/IP stack and network drivers, and probably much more in order to be able to port bitcoind to it.

What I'm saying it's not this is not feasible, but it could get much more complex and costly than you think. And this calls for the main question: why? What would be the purpose of developing, building, selling, buying and running such a device, which can only give a very small benefit to the Bitcoin network and can't perform any useful function at all for his owner?