No doubt that it could, in fact it couldn't avoid doing that, but the software is not designed at all to flag that kind of anomaly. LIGO has a supercomputer designed to comb the data looking for patterns that indicate arrival of a gravitational wave from outer space. A local disturbance would appear as noise to be filtered out.
Much of their analysis and tuning so far has been devoted to filtering out things like the ocean wave vibrations so the much smaller gravitational perturbations can be sensed. Both gravity waves and physical deformations stretch or contract the respective 2.5 mile arms you see in the LIGO photo and it is a painstaking process to separate one from the other. Local g disturbances would further complicate this and may have to be taken into account by the research team if they haven't already.
Software could no doubt be designed after-the-fact to flag local g anomalies for earthquake prediction purposes but I doubt this would be the optimal approach. Also, part of the reason LIGO was situated at Hanford was because of the relatively stable basalt underneath.