Appropriate to use connection?

I’ve been on 3 interviews for a department manager position at a major retail corporation. Everything seemed to be going great, but I haven’t heard back in over a week. (They said it would be a few days) The Senior Vice President of the company is a family friend of my husband’s family. I have only met him briefly on 2 occasions, however my husband’s parents said him and his wife spoke very highly of me. He is so far unaware that I’ve been interviewing there. Would it be appropriate to reach out to him if I don’t hear back from anyone? If so, what would be the best thing to say?