But can Spanish barba also mean English "barb," at least as in the context of writing or speaking critically of something? I think it may, as barba may also translate as "quill" or "quill point," meaning "pen," and by extension "critical pen," or the writing produced by a critical person.
The phrase I have in mind was cited by a visitor to Argentina. The visitor was a well-known critic of just about everything in the known world, and one reviewer mentioned the visitor's sarcástica barba. The visitor was indeed bearded. So did the reviewer mean that the visitor had a "sarcastic beard, therefore "sarcastic face," therefore sarcastic demeanor or attitude in general? Or did barba mean, in metonymy, the visitor's writings, his pen, his critical "quill," his sarcastically barbed criticisms?
Answer: Barba does indeed mean "beard" (or "chin") in the most common usage. And you're right that it can more generally refer in some idioms to "face" or even one's personality in general. (One way of saying "per person" is por barba, just as we might say "per head.") Among phrases using the word are con toda la barba, which is a way of saying that someone is everything he or she should be. And barba a barba is the equivalent of cara a cara, or face to face.
So in the context you mentioned, unless some sort of pun was intended, or unless there's some local idiom not familiar to me, the person probably meant simply that the man was in general sarcastic.
But there is a connection between barba and "barb." Hacer la barba a alguién (literally, "to do the beard to someone") can mean to bother someone. (It can also mean to shave someone.) And in English, a "barb" is a pointed remark often meant to bother someone. And it is worth noting here that the word "barb" comes from the Latin word barba, which is obviously where the Spanish word came from. But the connection between barba in Spanish and "barb" in English is one of word history (etymology), not one of meaning.
