By attempting to impeach Trump, Democrats will accomplish either of two things.
They will succeed in removing him from office. Mike Pence takes over. A career politician, well liked by conservatives, and somebody who will take on the 2020 elections with confidence. At this point, one must wonder whether facing Trump in the 2020 elections is the better choice than facing Pence...
They will fail in impeaching him, thus serving Trump yet another victory, and possibly giving him a boost for the 2020 elections.
It's a lose-lose situation, it seems.
So what is there to gain politically for the Democrats here?
There are three problems with your question that I believe is limiting your ability to grasp the goals of the various components of the various members of the national Democratic party.
The first is that you are viewing this as a straight gamble or bet where the payoffs map one-to-one with the strategy employed. To give a more financial example, a chance to win $50 if you are homeless is a profoundly different thing than if Bill Gates or Warren Buffett are given a chance to win $50. Equal payoff do not mean the same thing to two different people.
To give a political example, Max Baucus of Montana largely built and pushed Obamacare through Congress even though there was a preposterously high probability it would end his political career. It did. The payoff to Baucus was in tens of millions of lives improved. If you enter public service to improve the world and you finally get the chance to make a difference, even if it ends your career in service, many many people would do it.
Members of Congress are required to take an oath to support the Constitution. Some members have done so in combat. There is currently one presidential candidate who has been recalled to active duty. For some members of Congress, they are as willing to lose their jobs as to lose their lives to protect the country. If impeachment destroys them, so be it. The nation must be governed in such a manner that the Constitution is defended.
The second problem is short term versus long term thinking. You are framing it in terms of the 2020 election. Any career politician will tell you that a career is much longer than the next election. Careers do not end with a loss in an election. Democracy has to survive for elections to happen. Republicans have been up to a lot of shenanigans since the 2000 election.
It started almost by accident. Most elections are won by a very small number of votes. In Ohio, Republicans radically reduced the number of voting machines in the 2000 election in democratic precincts. There were lines to vote that ran until 3 am. Many people just walked away. Actually, thousands walked away. Al Gore lost the US election by one vote per precinct in Ohio. People focus on Florida but that was not the interesting case. Since then it has been obvious that Republicans have been attempting to restrict the vote everywhere they can.
That is pragmatic. Prior to Trump, the Republican party was dying off. The crisis was how to get new members when fewer and fewer people were registering Republican. The number of Democrats in the U.S. as a percentage of voters remained unchanged, but the number of Republicans fell dramatically. It wasn't that they were becoming independents. It was that they were graying, balding and then dying.
If Democrats impeach Trump and lose the 2020 election to Bill Weld, who among current Republican candidates for President is the most likely to carry broad support and pick up Democratic votes, they will have picked up the 2022 election as the next battleground.
To someone like Mitt Romney or Nikki Haley who could also win in 2020, the goal isn't the next election. The goal is to win it all or stay in forever. It does mean you want to win in 2020, but Lincoln lost his congressional seat and then came back to win the Presidency.
The third issue with your post is the role of Mike Pence. Pence may be a good candidate in 2024 but he is a terrible candidate for 2020.
Once impeachment starts, it won't be a question of whether the courts let the Congress have free reign on data. It will happen. The President cannot interfere with having free access to everything in an impeachment case. His tax returns will be handed over. His phone records will be handed over. The Attorney General will likely be impeached and there is a reasonable chance Rudy Giuliani will find himself under criminal investigation. Every embarrassing phone call and bad decision will be on television.
My earliest memory is breaking a window when I was 2 years old. My second memory is men landing on the moon. The third memory is Nixon's impeachment hearings. They bored me to no end but the adults kept watching them.
Republican members of Congress have had to be careful because Fox has been censoring the news. I do not say that as an accusation. I assigned 20 people to watch Fox, Rachel Maddow and PBS New Hour. While I can give you a whole boatload of reasons Maddow is irritating to viewers when required to watch her for hours and hours, one thing you can see is what isn't being said on Fox.
If every broadcast and cable news channel is broadcasting the hearings and Fox is selectively doing so, then Fox viewers will go elsewhere. That will change the dynamics for Republican elected officials.
Based on what is currently in the public record, Pence is a bad 2020 candidate. He is a good 2024 candidate but a bad 2020 candidate. He also was a middling politician anyway. He was always more of a John Delaney level candidate than an Elizabeth Warren level candidate to have a democratic comparison. He is pretty good but not great.
If I were a democratic candidate running for office and I had a choice of running against Mike Pence or Nikki Haley, I would choose Pence any day. Haley could win and would bring enough democrats over to shake the party. Pence would galvanize opposition.
Pence was likely betrayed early in the transition by those that really understood what was going on. He made decisions though and those decisions are going to look to Republicans as well as Democrats like really bad ones. He can claim ignorance up to a point. He would have to claim that he was the Vice President but completely left in the dark. If that is true, then he has no positive experience related to his role as Vice President except to be made a fool of. If it is isn't true, then he will be vilified.
In 2024, if Weld or Haley do not end up as President, Pence could win. Pence could go to Trump's base and say "Trump is a bad person but his goals were still good. He couldn't pull it off because he was so limited but I can."
Trump would cripple Pence the same way Clinton crippled Gore.
Finally, Trump has a strong interest in running for the presidency in the 2020 election even if he is impeached and even if he is not nominated.
Based on the contents of the Mueller report, he needs the statute of limitations to run out on him. It is unlikely that he would be prosecuted while a candidate. It would split the Republican ticket and Democrats would win in a landslide.
With all of that said, both of us have ignored one thing. If the House runs this slowly and carefully the news services are going to go bonkers. They will get ahead of the story just to have something to report. They will dig just to say they got it before the House did. They may start looking closely at senior Republicans in a way that is not normally done. For example, they may look at that Russian owned factory suddenly announced in Kentucky. They have touched it a little but they haven't spent two hours a night on it.
This has the potential to be like influenza. It could spread from Trump to key Republicans. If I were Fox News, or rather if I were Roger Ailes ghost, I would have started the process of immunizing the Republicans that I liked. I would give the non-commentary news branch free rein to report readily confirmed facts. It would give them an air of authority because they wouldn't be reporting speculation. I would begin preparing the base for a shock because of the things they have previously not heard about Trump.
I would try and make my base feel good about themselves in the commentary section. I would talk about the nobleness of pursuing ideals even with flawed instruments like David King of Israel. I would talk about the risks using those flawed instruments bring and how it has gone bad in the past. We picked up the dice, we gambled, it went badly. He was just too flawed. It is sad. Let us find a good replacement here on Fox.