The above stats suggest that the flight is at least fully booked, if not overbooked. If that situation remains, it will be oversold at the gate. But, UA and other carriers routinely overbook, yet oversales are few and far between and denied boarding even less so.

Whether you have a seat assignment is not relevant to whether you will be boarded so long as you show up on time.

If the flight is oversold, UA will seek volunteers to be off-loaded and if that fails, it will involuntarily deny boarding in a pre-specified order. The chances that a 1K would be anywhere near the top of that list are inconceiveably small.

I would nonetheless keep checking for an empty seat, check in at T-24 and be early to the gate. Also, bear in mind that UA holds seats for handicapped, families and the like. Thus, there could even be seats available which are not ready for specific assignment.

All of the above said, it is possible that you will land in a lousy seat. Me, if there were alternatives, including a connection, with good seats available for selection, I would grab that.