There is a lot of anecdotal evidence that one could give to support the theory that having an ace gives you a better chance of winning in the postseason. However, according to a study conducted at Baseball Prospectus (and other studies), the correlation between having a top notch pitcher and postseason success is .02 - statistically insignificant.
Here is a the pertinent part of the study, along with a link:
"To do that, BP Director of Research Colin Wyers selected the “ace” of each playoff team from the one-wild-card era of 1994-2011, defining the ace as the starter who pitched at least 120 innings with the lowest ERA. Then he came up with a normalized measure of “ace-ness,” similar to ERA+ (2-ERA/lgERA, to be precise), that allowed us to place all the aces on the same scale. Finally, he checked the correlation between the strength of each team’s ace and the difference between its winning percentages in the regular season and the postseason.
The result? A statistically insignificant .02. Park-adjusting the stats didn’t strengthen the correlation. Neither did defining “ace” as the starter with the highest WARP. Neither did running the study again using only pitchers who pitched in the playoffs, so as not to skew the results by including teams whose regular-season aces weren’t available in October. However we sliced and diced the data, we couldn’t find any evidence that the strength of a team’s top starter alone helped dictate how it would do.
"
http://www.baseballprospectus.com/article.php?articleid=18414
Granted, this might change as the scoring environment changes, but as of now, there has been no significant evidence supporting the "ace" theory.