Does English have a version of "pouring water on a goose"?

Different localities have their own phrases that match this, but some more "universal" English ones I can think of are:

• "A wild-goose chase"
• "Pissing/spitting into the wind"
• "A fool's errand"

Also the following might fit similar situations:

• "As useful as a chocolate teapot" (refering to a useless object)
• "Like hearding cats" (a task so difficult it's pointless)
• "Getting blood from a stone" (sometimes used to describe the futility of getting information out of someone)

Exactly as @Yosef Baskin has said in a comment, this translates perfectly from goose to duck in the phrase like water off a duck's back.

(like) water off a duck's back
informal : having no effect on someone
He tried to convince her to take the job, but his advice was like water off a duck's back. Merriam Webster

This tangible metaphor and/or simile shows how one can be unaffected or impervious to an event, like the idea behind outcome independence. The ducks, like the geese, do not let the water stick; they take it as it comes and keep on going.

Pouring water on a duck to as useless as a chocolate teapot or to keep with the aquatic theme, a fish with a bicycle; it's pointless.

Dunn's modesty is appropriate, as 'A needs a B like a C needs a D' was a well-established format in the USA many years before 1970; for example, this usage in the Connecticut newspaper The Hartford Courant, December, 1898:

The place [Aragon, Spain] didn't need an American consul any more than a cow needs a bicycle; for it had no trade with America, and no American tourist ever dreamed of stopping there.

Or this, from The Detroit Free Press, October, 1906:

The house didn't need a fire then any more than a horse needs a shave.