Is it grammatically correct to conjugate "someone has" as "someone's"?
As in: Someone's walked off with my coat.
Yes. This is common in speech (and therefore in written dialog); it would be uncommon in an essay or other text outside of quoted speech.
It would be passably correct, but incredibly awkward, for example to write "The United States's been getting a bum rap lately," but that is the way we would SAY it.