The dangling error in the earlier data presentation was that we added up the total number of walkoff games erroneously. There are actually 57 such games, not 56 as reported earlier.
OK, we won't let the answer dangle in the midst of this mea culpa. But the answer is rather surprising--or it will be for those of you who expect the results to reside in coin-flip territory.

What's that winning percentage, you ask? You can see it in the chart (above right): it's .684, or 39-18. Winning WS teams have won more than twice as many of the walkoff games in the WS. (In the chart, teams winning walkoff games who went on to lose the WS are shown in red.)
Even when you remove the "bias" of the walkoff win in Game 7 (or, for 1912, where there was a tie, in Game 8), the winning team in the WS still has a sizable lead (33-18, .647).
As you might suspect, the Yankees have been in the most walkoff games in World Series history--a total of 20. Their won-loss record in those games? 12-8. The Dodgers are next with nine walkoff games: their record is 3-6 (2-4 against the Yankees). Remember that these are overall records in walkoff games: the Yankees' record in walkoff games in which they won the WS is 9-3; the Dodgers' is 3-1.