I was going to say that I liked your avatar. Since GD already answered really well on the predators, I'll address the dog.
You probably know your dog best. If he wants to CHASE the geese, and he's 12 years old, I wouldn't bother to try training him. If he doesn't want to chase them, and is a generally protective dog, he might want to protect them. BUT, if you are not cooping or penning the geese, I suspect they will worry and annoy him much of the time, and outright attack him during breeding season. Even a saintly dog will probably tire of the provocation. The only way he will probably be able to defend them is if they are in a coop/pen and he has full access AROUND them. (and with no overhanging branches out of his reach, especially if raccoons are a concern)
Even so, I don't use my dog that way. My geese can see out of their coop, and would put up a HUGE fuss if he even came to their side of the yard. I'm sure it couldn't be good for the geese to be so agitated so much of the night. I have a llama that I release into the goose yard at night. She doesn't agitate them and wouldn't let a coyote in without at least raising an alarm. Coyotes are my main concern (unless weasels ever become a problem) as their coop should be safe from everything in between.
But unless your setup is perfect for it, I wouldn't hold a lot of hope.
Raising a dog with the geese won't help from the goose's point of view, in my opinion. During breeding season, they are still going to know it's a dog and won't allow it around without a fight.
So, my llama watches the geese and nearby rabbits at night. She's in the backyard, and the dog watches the llama through the window. If anything happens and I don't hear it, he WILL let me know. In my situation though, secure coops, hutches, etc. during the night are the most important deterrent.