Perhaps it is more accurate to say that sarcasm is a way to express cynicism. At any rate, yes, they're related. Maybe not unhealthy to be cynical - unless one is cynical about (just about) everything.

Reminds me about the joke about the politician - how can you tell when the politician is telling a lie? (The answer: when he opens his mouth to speak

Recently, that's about the way it is with me & sarcasm.