Just the AFC teams (I just don't feel like doing it for the whole NFL but it's going to be basically the same).
Mia: 56 seasons in SB era, 13 HC, 2 SB titles, 1 SB-winning HC
Buf: 56 seasons in SB era, 18 HC, 0 SB titles, 0 SB-winning HC
NYJ: 56 seasons in SB era, 18 HC, 1 SB title, 1 SB-winning HC
NE: 56 seasons in SB era, 14 HC, 6 SB titles, 1 SB-winning HC
Bal: 26 seasons in SB era, 3 HC, 2 SB titles, 2 SB-winning HC
Pit: 56 seasons in SB era, 4 HC, 6 SB titles, 3 SB-winning HC
Cin: 54 seasons in SB era, 10 HC, 0 SB titles, 0 SB-winning HC
Cle: 52 seasons in SB era, 21 HC, 0 SB titles, 0 SB-winning HC
Jax: 27 seasons in SB era, 9 HC, 0 SB titles, 0 SB-winning HC
Hou: 20 seasons in SB era, 8 HC, 0 SB titles, 0 SB-winning HC
Ind: 56 seasons in SB era, 21 HC, 2 SB titles, 2 SB-winning HC
Ten: 56 seasons in SB era, 15 HC, 0 SB titles, 0 SB-winning HC
KC: 56 seasons in SB era, 13 HC, 3 SB titles, 2 SB-winning HC
LAC: 56 seasons in SB era, 16 HC, 0 SB titles, 0 SB-winning HC
Den: 56 seasons in SB era, 18 HC, 3 SB titles, 2 SB-winning HC
LV: 56 seasons in SB era, 19 HC, 3 SB titles, 2 SB-winning HC
So these 16 franchises have played a total of 795 seasons in the SB era, have had 220 HC, have won 28 SB titles, and there have been 14 SB-winning HC.
14 out of 220 HC in the history of the AFC in the SB era have won Super Bowls. That's 6.4%. That means that 95.4% of all HC in the AFC during the SB era did not or have not won a Super Bowl, over the course of 795 combined seasons.
So yeah, while I don't KNOW that the next non-BB coach the Pats hire won't win a SB, it's a pretty good bet that he won't.