Update:
Less than two weeks after I applied, I was notified that my application had been tentatively approved and that I needed to come in for a face-to-face interview at the Global Entry office at Miami international Airport. I went the next day and was approved on site. Therefore, it took me two weeks from start to finish to apply for and get approved for the global entry program. I took my first trip a week later to Chicago. Although I did not get TSA pre-on the outbound flight, I did get TSA pre-on the return flight. I've been told that being a member of Global Entry will likely get me TSA pre-often.