I have two American Buff geese. I can tell you that their vision is incredible and they are always watching. They screech a warning when they see something that the other birds don't. In that regard, they are quite impressive.
That said, my birds were performing some garden cleanup services yesterday, and the resident Holland lop was out of his pen running about. They freaked out. Hissing, wings out and shaking... Nibbler, the nonplussed rabbit, went right up to them and sniffed one. They ran, screaming, away.
Geese are not really able to offer protection services. They may deter certain types of predators with their size alone, but are not really able to do anything other than that.
The only real defense against hawks and other birds of prey is cover.