My job interviewer was not in HR or the hiring manager. Should I reach out to the HR director to express my gratitude and interest personally?

Anonymous
I had an interview with an employee who was not HR. He hinted that a few times. However, he was the person to contact for a follow up. I did and he told me HR was still working on it as it’s taking a bit longer than expected (and that it’s not unusual for HR to be delayed). While he was my interviewer, would it be ok for me to reach out to the HR director and express my gratitude and interest, and thank them for their time and consideration? I was not given the HR director’s name or any contact info however. But I did find their name on the company website and with a Google search, I found their email. Would it be considered annoying or pushy if I did reach out or would it demonstrate interest and dedication?
My job interviewer was not in HR or the hiring manager. Should I reach out to the HR director to express my gratitude and interest personally?
2 Opinion