With a mobile MQTT client, absolutely! This list gives examples of both iOS and Android MQTT client applications. One of the cool things about MQTT is that the platform itself doesn't hold you back; once you've got the broker running, as long as you have a client implementation you can communicate mobile-to-mobile, mobile-to-PC, PC-to-PC, etc!

That's a great question, Jason! I'm not quite sure how/why this project was posted to the BeagleBoard community... but since BeagleBones are pretty powerful little linux machines, one could easily replace the Raspberry Pi in this project with, say, a BeagleBone Black. That would be especially useful if you wanted to have the MQTT broker doing other things as well - since the BeagleBone Black is more powerful than a Raspberry Pi, I'd imagine it would perform better at handling a number of other tasks in addition to the MQTT broker.

For anyone interested in doing this, a quick Google search gives a number of tutorials for setting up MQTT on a BeagleBone (it should be pretty similar to what I described above, since you can run Debian on a BeagleBone).

Make sure that you're using version 0.12.1 of Arduino's WiFi101 driver! If you use the latest version, the Due will get hung even before checking the status of the shield. Happy building!