Yes Grey herons can and do eat rats when they need too.
The grey heron prefers other prey such as fish but when they see a rat and are hungry the grey heron will swoop down and scoop up the rat and eat them.
I've seen grey herons or at least one grey heron at a park one day swoop down and catch a rat and take off with it.
So yes the grey heron does eat rats.
Blue herons and other herons will also eat rats although their diets consist mostly of fish which they get by hovering over the water and landing feet first into the water to get the fish and then take off with it.
Herons including grey herons and blue herons are great and wonderful swimmers.