My mom used to use the expression dumb as a post, but I guess maybe deaf as a post might be a thing too. Posts don’t speak or hear was probably the origin, but my mom used dumb as a post to mean the person was stupid, and I think that would still be the common interpretation today in America, since dumb is most frequently used to mean stupid, and mute is more typically used to signify unable to speak.
Anyway, I’d say yes, posts are deaf.