Yes, the Saints and Panthers currently are tied atop the NFC South, with four games left to play — two of which will be played against each other. Assuming New Orleans otherwise beats the Rams and Bucs and Carolina otherwise beats the Jets and Falcons, the Panthers will need to sweep the Saints to win the division, which likely comes with a first-round bye.
Assuming that the Saints and Panthers finish with the same record, a split of the two-games-in-14-days series will result in the Saints winning the division (and the likely bye) via the fourth tiebreaker for teams in the same division, record within the conference. Because the Saints have lost two of their three games to AFC East teams (the Jets and the Patriots), the Saints necessarily have a better record against conference opponents, since the Panthers have lost two of their three games to NFC teams.
If the Panthers sweep the Saints, the Panthers would win the division on the first tiebreaker, even if the Panthers lose their other two games.
It likely would be better for other teams in the NFC playoff field for the Panthers to pull off the sweep and win the division (and the likely bye), given that it would force the Saints to go on the road in the wild-card round — and it would allow one of the wild-card winners to avoid going to the Superdome in the divisional round.
So, in all likelihood, Sunday night’s game will determine the NFC South title, and the likely bye that goes along with it. For the Saints, that’ll mean quickly recovering from their drubbing in Seattle, and an even shorter short week, thanks to airplane trouble.