Here is an update after my conversation with the alumna. An interview may not help, but can definitely hurt. No real surprises in terms of what the school is looking for during the interview: intellectual capacity, community (and passion towards what you do outside of work), and finally career track record of success and realistic expectations what the MBA can do for one's career.
She mentioned there are three main reasons why she hasn't recommended someone in the past: No outside interests, not enough experience, or no clear reason of why they need an MBA
And one more thing she said I thought was helpful. She said that alumni interviews are sometimes so conversational, you may not even get asked the standard questions of why mba, why U chicago. However, you will be judged on that. So it is important to work those into the conversation.