Its not just a normal LAN. Beowulf clusters and the SETI@Home project involve computers networked together.
Anyway, I'm not sure if they are going to compute anything but they are going to benchmark it with Linpack.
If this actually works (and works well), then that would mean people who have plenty of standard personal computers but need more computing power for certain problems could LAN their computers together and boot up the software being designed for this project.
As a side note, there is a version of Knoppix called
ClusterKnoppix that is meant to do stuff like this, so I'm assuming the people behind the Flash Mob project have come up with a better way of doing it.