There are 36 fewer total possessions in an average Virginia game (#351 tempo - last in country) than an average Kentucky game (#17 tempo). That's a drastic difference.
Theoretically, this should give underdogs a better chance to win against Virginia than against Kentucky, since the efficiency margin results in a smaller score margin in fewer possessions, and the 30-40% event of any given 3 going in needs to happen fewer times for the underdog to close that smaller score margin against Virginia.
However, empirically, just eyeballing the kenpom archives, this doesn't seem to hold through the NCAA Tournament since 2005. A sub-100 tempo team has won the national title every season since 2005 except for 2009. Maybe when it comes down to individual games against more evenly matched teams, the slower team is at an advantage because it's much easier to slow down the pace to what you're comfortable with than for the opponent to speed you up. And the close matchups not only occur in most tournament games (unless you're 2016 UNC), but they're also the more important matchups to have any sort of advantage in. Playing against a significant underdog in round 2, Virginia may have a greater chance of being upset than Kentucky due to score margin, for example, but we're talking about the difference between something like 20% and 25%. You'd take that "disadvantage" in round 2 if you're Virginia in exchange for the head to head advantage in a Final Four game against Kentucky when you can slow Kentucky down to a pace they aren't comfortable in.
Interestingly, the fast teams dominated from 2002-2005. Maryland 02, Syracuse 03 and UNC 05 were each no worse than #34 in tempo, and UConn 04 was top 100. There appears to be a trend of slower and slower teams winning titles, perhaps because of a talent drain (due to more frequent early NBA departures) that has led to more elite teams playing slow styles, which means elite teams that play fast are at a disadvantage more frequently in the NCAA Tournament.
Duke seems to prefer a slower style with Matt Jones snailing the ball up the court every possession, but Duke can also speed the game up against a team like Virginia. All K needs to do is play 10 guys and go with a full court press, trusting his usual bench warmers at spots 8-10 in the rotation (currently Bolden, Giles and Jeter) for 8-12 minutes a game. Lol.