When we went just a week and a half ago the theater was only half-full after allowing in every standby guest. It was a midday show, I think 3:30'ish. No one can promise you 3:15 is okay, but based on my experience it would be fine. By 3:15 in the day you'll probly be improvising so I'd play it by ear and know you can get in to a later showing even if you're busy and miss this one!
If it is critical for your schedule that you make this particular showing, I would plan to be there at 3:00 and not leave it till 15 min before showtime. 15 min prior they let the outside standby line into the covered section where you line up by the theater doors. Then you watch Frozen clips for 15 min while you wait out that last bit.