Hmm. I was curious, so I looked at all the playoff games and SBs going back to 1983. I've looked only at games where each team had only one QB that threw a significant number of passes, just to make things easier. That's 278 games. In 201 of those, the QB with the better TD/INT ratio won (in another 24, they had identical ratios). In 216 of those, the QB with the better passer rating won.
I adjusted the numbers so that a 0 TD, 1 INT game is better than a 0/2 game and also so that a 2/0 game is better than a 1/0 game. Also, a 0/0 game is the same as a 1/1 game. The results are the same whether you make those adjustments or not: the passer rating identifies the winner more often than the TD/INT ratio.
Now, this doesn't account for QB fumbles. So I checked games where the TD/INT ratio and passer rating were both "wrong" to see if the TD/QB turnover ratio was "right". There were 39 of these games. I checked the most recent 16 of those, and one game flipped (another went from "wrong" to "same"). It's pretty clear to me that TD/QB turnover ratio does not correlate with victory in the playoffs/SB better than passer rating does in any significant way, and in fact the reverse appears to be true.