Geese aren’t going to do anything about the rats, geese don’t eat them and aren’t fast enough to catch them.
Geese will not deter predators or protect your flock from predators either.
Geese are smaller and more fragile than they advertise themselves to be, they cannot defend themselves let alone others from even small predators like foxes or raccoons.
What geese can do is deter hawks because of their size and presence, all the hawk registers is that it sees a big bird and wants to avoid it. Bolder hawks and eagles are not fooled though.
If you want real protection a dog is more effective.
Geese aren’t prejudiced against breed or gender. You can have two girls or two ganders just fine.