To be honest, if anything, Gore would lose by a larger margin in 2000. The GOP squandered alot of its political capital trying to get Clinton removed from office. Without that, the Republicans certainly would have gained seats in Congress in 1998, and once that happened, George W. Bush may not have even been the canidate in 2000.
I think this is a very fair point. Gingrich's pursuit of the impeachment really derailed the House leadership, and hurt the Republicans in the eyes of the public. This is evident in the poor GOP performance in the '98 midterms. The year should have seen some moderate gains as Clinton suffered from the 6 year itch. When I can be bothered, maybe tomorrow, I might look into the close races of '98 and see how many more Senators the GOP could have had. Don't know if D'Amato could have held, but Faircloth would have and Matt Fong may have done better against Boxer.
As for 2000, Bush made much of his early campaign about character. Without that being such a pressing edge, it could butterfly away his advantage over McCain, or possibly encourage him to listen to Rove and get the DUI information out earlier when it would be less damaging. The latter reportedly involved Bush's personal views as to how his daughters would react, so I can't say that would happen for certain.
By the way, I expect most agree that this wouldn't change much for Gingrich's career. Even without impeachment proceedings, the ethics violations and own extramarital affair still happens. Gingrich looks like less of a hypocrite on the latter, if he doesn't pursue Clinton as hard, but he still remains a polarizing liability. Although he doesn't suffer the indignity of losing seats in the House, the plans to drop him as Speaker were well underway before then.