The reef itself is built on continental crust at the edge of the Australian plate where it borders the Coral Sea basin. The continental crust itself is not very prone to earthquakes, but because of all the relatively nearby tectonic activity (subduction arcs to the northeast and north) there is still some minor and occasional earthquake activity in the region of the reef.
Basically, subduction to the northeast (with the Pacific Plate) caused flexing of the crust on the west (Australia) side of the plate contact (the subduction zone), and this resulted in the opening of the Coral Sea (a back-arc basin) and flexing of the crust on the east side of the Australia plate (there was uplift of the Great Divide that marks the east side of Australia, and the area of the reef is kind of a hinge zone between the two: the down of the Coral Sea and the up of the Great Divide).
So there is some earth movement and some earthquake activity. It is not a highly active zone, but it isn't quiet either.
The answer is always "yes" to the question "are there earthquakes in area XXX ?" Just a question of how frequent and how big. Earthquakes happen pretty well everywhere, once in a while.