Not protected in all jurisdictions.
And generally hunting laws are hard to enforce. If I were homeless in Vancouver, BC I'd be going after geese.
Note however: the reason that Canadians generally are such nice people, is that we transfer all our meanness into our geese and send them south for hte winter.
Anyway, a blow from the wing of an annoyed goose can break your arm, and they can be quite agreessive with their beaks.
In most jurisdictions you cannot hunt birds that are on the ground. I suspect that this is mostly a safety rule. Birds are small targets, usually hunted in relatively flat, fairly open ground. A bullet that misses the bird can hit something (or someone) else. If the bird is on water (A sitting duck) bullets ricochet very nicely off of water. Overall it's a sensible rule.
If you wanted to try this:
- Shoot on land.
- shoot down, so that bullets that miss the bird hit dirt soon. You will need to be pretty good with a .22 to succeed at this. Ideally you want head shots.
If I wanted to try to have fresh poached goose for supper, and for winter Sunday dinners, I would practice with a bolo, or with a trebuchet launched net. Or by finding a favoured glide path and put up one of those nearly invisible deer fences, but run it as high as you could.
If in a park where they are used to people, a noose on the end of a stick, like dog catchers use, might work.
It may be possible to bait and snare them.
How did First Nations people's get them before they got firearms.