Democrats are happy about impeachment because Donald Trump is their political rival, and they think it is nice to see their political rival get a stain on his record. Regardless of what happens in the Senate, he will forever go down as just the third president to be impeached.
However, the more important reason that Democrats are happy is probably because they think this will help them win in 2020—and perhaps it will. It was a political gamble taken by Speaker Pelosi.
Conventional political wisdom dictates that impeachment is bad for the party that impeaches because it fires up the opposition and makes it look like your party has no interest in governing. This wisdom is confirmed by the fact that during the 1998 impeachment of President Clinton, Republicans lost seats in the midterms. Most political scientists have looked back at the 1998 Clinton impeachment as a losing battle for Republicans.
But there is one thing that these political scientists and historians seem to forget...
While Republicans lost the 1998 midterms, two years later, they won the prize that really matters—the White House! Democrats won the battle, but Republicans won the war. With a thriving economy, a budget surplus, and years of remarkably low unemployment, the 2000 election should have been a slam dunk for Democrats. But it wasn't. While Al Gore narrowly won the popular vote by less than a half percent, George W. Bush won the White House, and Republicans held onto both chambers of Congress, giving them full control of government. The reasons for this are many, but not the least of which is that Al Gore needed to distance himself from Clinton after all of the scandals that plagued his presidency. When then-Governor George W. Bush campaigned, he always ended his rallies with a line to the effect of "I want to make a promise to every American that if given the chance to serve as your President, I will uphold the honor and the dignity to the office of which I'd been elected." That was a subtle reference to the whole Clinton impeachment. Americans didn't think President Clinton should be removed from office, but they also didn't think that having an affair in the Oval Office with a White House intern was appropriate conduct for the highest office in the land. They felt Clinton was not upholding the honor and dignity of the office. In other words, Republicans managed to make his affair with a White House intern enough of an issue that it
created a scandal.
There is an American University professor that built a model that has correctly predicted every single presidential election since 1984. It uses 13 true/false statements with the basic premise of this: if the country is doing well, the incumbent party remains in office, and if the country is doing poorly, the opposition party is elected. One of the true/false statements is this: "The incumbent administration is untainted by major scandal." With this impeachment, this will have to be marked as a false. In other words, Democrats have managed to
create a scandal just as Republicans did in 1998 and 1999.
We know that the Senate will vote to acquit. The real vote will take place in November of next year, and that will be when we determine whether or not President Trump will be removed from office.
So to answer your final question, I think it will certainly look bad for Democrats if they impeach Trump and then he is re-elected, and history will likely remember their impeachment the same way it remembers the Clinton impeachment—as political grandstanding. Personally, I don't think that Democrats are impeaching because they think next year will be a slam dunk. I think it's actually quite the opposite. Democrats are acknowledging the very real possibility of Trump's re-election, and Democrats want to do everything they can to give themselves every advantage possible come next November to avoid a repeat of 2016. Democrats hope it will turn off his base and fire up their own base.
We will find out next November if they were right