Can you elaborate why it's gauche? I'm assuming the intent is to share on the platform that has the audience you are seeing to share the message to. It's not user friendly to direct people to another channel.
Alternative take: Twitter is where people are and information spreads by push vs having someone discover/navigate/link to your personal site for the announcement.
12 tweets is certainly a lot though but I don't get the idea that using Twitter to share important news is gauche. Maybe that was the case when they first launched but certainly not now.