in my experience, it depends...
I've had some geese that would protect whatever birds are there. and some that protect only other geese *from* whatever other birds are there!
in my experience, geese will protect what they're raised with. I've got a small group of 5-month brown chinese geese, and they stick to them selves, mostly ignoring the other birds (ducks, chickens, turkeys, guineas). while not agressive, they'll occasionally pinch some bird that's between them and the feeder.
I've got one 2 1/2 month african that was raised with ducks of the same age, and he hangs with and protects them, warning off all the other birds. I think he's starting to figure out that he's a goose, not a duck, because sometimes he'll do the flight-run with the bigger geese, but he hangs with, forages with and protects the ducks.
Saw the same thing growing up, we had geese and ducks, and each year the geese would protect the ducks they were raised with and run off the geese and ducks from other years. of course, ALL the geese ran off our poor collie, who wasn't quite bright enough to figure out the geese were NEVER going to be happy to have him licking them.
so... I'd say your best shot is to raise the goslings with the babies you want them to protect, all in the same brooder. If those birds hatch babies, I'm guessing they'd take on protecting offspring as well. we never kept chickens so I dont' know if they'd adopt them, but if they were raised together, they might well do so.
In general, my geese will challenge, but not "fight off" animals or people they don't recognize, so the other birds get some protection because the geese are alert about intruders in the yard. We had one african goose as a kid that would actually defend - pinch you or beat you with his wings (OUCH!) - but most of them, while quite loud about intruders, were all honk and no bite. kind of like the difference between a watch dog - who'll notify you of intruders - and a guard dog - who is prepared to do something agressive about it. Mostly my geese are much better about warning than actual guarding.