The Hydrated lime will readily dissolve in water, but the Alum never truly dissolves, it becomes a slurry and will need to be stirred a lot at first and then occasionally during application. The Alum slurry will always have a few stubborn granules but your sump pump won't have a problem.
I wonder more if the pump will be able to develop enough pressure to spray the needed distance from the shore. The best "spray pattern" is a fan shaped spray.
I personally use a boat equipped with a boomless sprayer to clear client ponds. A small gas powered trash pump with the outlet necked down to a 1/4" pipe nipple tat has the outlet end smashed nearly flat and closed works well also.
