Cleavage causing earthquakes....well, if the cleavage of the minerals making up the rocks along the fault is trending broadly in the direction of the slip planes within the rocks, then that'll make the rocks more prone to breaking along those slip planes if pressure is put on them. Usually, you'll get recrystallisation of the minerals within the rocks if you get enough strain occurring and those minerals will subsequently trend in their orientation in the direction of the strain. Any previously existing structures, such as sedimentary bedding, unconformities/disconformities, previous faulting, mineral layering and flow banding etc etc etc, will be deformed and can create further weakness within the rocks.
So, in geologically correct terms (notwithstanding other forms of cleavage), the answer is...possibly
