You probably could do it, but it would not be economical. You would be limited by the solubilities of the various compounds such as calcium sulfate.
In a typical FGD, you have a recirculating loop. Because of the higher dissolved solids in seawater, you probably could not recirculate. To maintain the maximum solubilities, you would probably have to add chemicals on a once through basis. That would not be economical. It also goes without saying that the equipment cost would also be expensive because you would have to use materials that would stand up to seawater.