It is possible to win with an average qb but it is very rare in the NFL. Solid RB, play action, and stellar defense describes like every Schottyball team, but they were all missing great qb's and found ways to lose in the playoffs. I have seen plenty of these teams from the Steelers in the 90s and early 00s and those teams were really good, but the problem is that when you get behind you have to change you plan and put the game in your qb's hands. Small handed and average to below average qb's so very rarely come through in those circumstances and it makes the degree of difficulty of winning a SB without an elite qb almost impossible.
It can happen, but a lot has to go your way because in almost every playoff run there is going to be one game where something goes wrong on offense or defense, and the other unit has to bail the team out. Once you get behind it is really tough to run your way back into the game in the playoffs.
Then again being lucky as fuck is probably the best way to win the SB these days. Regular season means shit. Just get in, have a qb with a hot hand and with a few breaks your team could be SB champion*.
* To avoid needlessly getting peoples' hopes up this does not apply to the Browns, Cardinals, Lions, Jaguars or Redskins.