here's what i got after putting it all together from 2002-2009 championships (both teams participating)
2009 UNC, lost ACC, won tourney; Michigan St., lost Big 10
2008 Kansas, won Big 12, won tourney; Memphis, won C-USA
2007 Florida, won SEC, won tourney; OSU, won Big 10, lost
2006 Florida, won SEC, won tourney; UCLA, won PAC 10, lost
2005 UNC, lost ACC, won tourney; opponent won conf tourney
2004 UCONN, won Big East, won tourney; GA tech, lost ACC tourney
2003 Syracuse, lost Big East, won tourney; Kansas, lost Big 12 tourney
2002 Maryland, lost ACC, won tourney; Indiana, lost conference tourney
Not sure how strong of a correlation would be one way or another honestly...