Well, after disappointment in finding the useful tennis databases failed to give match dates, decided to slog it out a bit to try to at least get you something slightly useful.
I used date-restricted Google searches (such as this one) and skimmed the news articles results that were known-legitimate publications until coming across articles showing the other semifinal was to be played the next day. And this is what I managed to scrabble together for the finals result (using Wikipedia for result) of those players who got the extra day off by playing the earlier semifinal:
2017: Federer Win
2016: Djokovic Win
2015: Murray Loss
2014: Wawrinka Win
2013: Djokovic Win
2012: Nadal Loss
2011: Djokovic Win
2010: Murray Loss
2009: Federer Loss
2008: Tsonga Loss
2007: Federer Win
2006: Baghdatis Loss
2005: Safin Win
2004: Safin Loss
2003: Agassi Win
2002: Johansson Win
2001: Agassi Win
2000: Agassi Win
1999: Enqvist Loss
1998: Korda Win
1997: Moya Loss
So if I made no mistakes, the extra rest lead the final match series just slightly: 12-9.
A slight advantage shown, but nowhere near statistically significant in that sample size (a binomial 95% confidence interval of winning anywhere from 34%-78%).
So, you'd absolutely need more data before a conclusion can be made. It may seem a hint that it has an impact, but it's quite possible that it has no impact (or even a losing one!)
And, indeed, such a trend could still be masked by seeding, injuries, and a million other things.
If I've run statistics right, it looks like you'd need well over 50 years of data to be able to have much hope of drawing any conclusion even in a large case, and even more if the impact is subtle.
But long story short: it appears all hints so far... is that I'm trending towards basically everything jamauss said!