Yes, the BS DOES deserve to know. I wish somebody had sent me an anonymous letter....I would have started watching H and OW sooner than I did.
Do send the anonymous letter and explain to the wife exactly what you posted here. That you have no concrete evidence only the word of a coworker because the slut has bragged about it.
Let the BS figure out what to do with it. If she is smart, she will be watching him like a hawk.