It sure is. Besides Olympiakos, PAOK is the only other Greek team that brought in any substantial points to the UEFA's coefficient. Without those points, the 12th position in the UEFA standings would have disappeared much sooner. Also PAOK in European competitions has quite a good points coefficient, which means we get easier draws and thus acquire more points for the overall standings easier. That's something AEK, Panionios, Tripoli, Giannina can't do.
As for the 12 smaller teams, half of those teams are in Marinakis's corner, and even with PAOK, AEk and Panathinaikos joining forces, there are not enough votes to overturn the "red" majority in the Superleague.