I think they still would have because if you recall the whole thing started with the Whitewater investigation that took almost 5 years and by some estimates, over $70m (between $39m and $70m depending on who you believe) to investigate. When they couldn't find sufficient evidence to charge Bill & Hillary in the Whitewater scandal, Starr grabbed on to the Lewinsky matter after Tripp delivered audio tapes of Lewinsky discussing her affair with Tripp....so yeah, I think they were out to get Clinton no matter what. The funny thing is, some of the Republicans that led the charge of impeachment were found to have been carrying on affairs of their own including Henry Hyde, Bob Livingston, Denny Hastert, Bob Barr, Dan Burton, and more incredibly Newt Gingrich who was having an affair with an intern during the time he was calling for Clinton's impeachment....