Late spring moisture levels primarily affect the number of berry flowers on each plant.  Dry years mean fewer flowers.  Early summer moisture affects how many flowers end up becoming viable fruit, and partially determine the speed of ripening though temperature has more effect than moisture on ripening speed.

I think it's safe to say there won't be a bumper crop this year, but if June sees normal rainfall then you shouldn't have to scrounge too hard for berries during the peak of ripeness, whenever that happens to be.