There are 2 15-day passes: 15 days within 2 months (flexipass) and 15 days (consecutive).

1. 15 days consecutive pass: no, that is not possible. The pass is not valid anymore after 23:59 on the 15th day.
2. 15 days within 2 months flexipass: that is possible, as long as your arrival date is still within the 2-month validity period. If you use the 15th travel day on the last day of the 2-month validity period, then it's not possible.