There are two known magma chambers in the Long Valley complex: one under the existing Long Valley caldera and one under the Mono-Inyo volcanic complex. Both are far enough away from the Hawthorne swarm to make it unlikely that they are directly involved. Of course, there COULD be a previously unknown magma source involved...
Look at the depths of the quakes - they are all very shallow. Were they representing magma movement they would be far deeper and generating distinguishing harmonic signatures. It is unlikely they are relating to the activation of a volcano.