Fyi, BN doesn't exist anymore. And by accounts and an increasing # of anecdotes the time you check in is irrelevant now. Yes, if you check in you'll get a low "SEC". However, no a low "SEC" # does not mean you have priority over another GO who is a higher SEC. That was the old BN system. Instead now, an internal "CIV" score determines the tiebreaker, and you don't know how your CIV compares to other GOs.

For your exact question, we probably need a bit more details...route, flight # would be helpful. Overall your chances are not high on any flight given all DMs will have priority over you, but still possible.