It only makes sense to do it if the national mood is that it has to be done, not that it's merely partisan spite like the well-poisoning Clinton episode. According to polls, the American public is still cool to impeachment.
Just like the shutdown, Pelosi wants to make sure that if she has to do the unpopular thing then she wants Trump to take the blame. If ALL the evidence is made available to the public and it can be made publicly accepted that Trump's lawsuits blocking subpoenas are forcing the impeachment, then I would be on board.
Trump should be impeached and it is disgraceful that this is even a question. This incompetent buffoon should have been impeached the day he stepped into the Oval Office. It is a sad state of affairs that somebody so deserving of impeachment can avoid it, solely because of political considerations.
But...Trump wants to be impeached, as soon as possible. The sooner he can get the impeachment hearings to McConnell, the better
Rather than impeachment, at this time, targeted hearings into Trump's wrongdoing will be helpful to the goal of getting rid of Trump. Hearings on every possible slimy facet of Trump's political, personal and public life. Benghazi the shit out of him.
I believe any sort of hearings McConnell might hold in the Senate - likely testimonials from "faith leaders" and other people willing to say that Trump is the most wonderful person walking the earth, etc. are going to be unhelpful to the goal of getting rid of Trump. Many on the left might assume that masses of Americans would react to such 'hearings' with disgust, but the fact is that masses of Americans aren't paying much attention to Trump's shenanigans, masses of Americans think Trumps disgusting but don't care and would take laudatory 'hearings' at face value. There are as many people who see impeachment as nothing more than an attempt to reverse the election results of 2016 and therefore oppose it. The "mealy-mouthed middle". These people don't care that Trump breaks the law.
It's very possible that sending articles of impeachment to the Senate would result in a vote of acquittal for Trump, which would be enormously helpful to Trump due to the large numbers of 'not paying much attention' voters as well as Trump's base. It's very possible that enabling a quick acquittal vote would be unhelpful in the main goal of getting rid of Trump. So, if by "the impeachment process" you mean a House vote to impeach, and then a Senate vote to acquit: no don't think that would harm Trump. But if you mean extensive, targeted hearings in the House, then, yes, I think that could harm Trump.
Pelosi has chosen what appears to be an unpopular track with the left. She does not want to cede the ground of impeachment to the Senate, where they can hold competing "impeachment" hearings while she simultaneously conducts "oversight" hearings. Once she loses control of the process, there is no coming back from her choice. I'm sure McConnell has some nasty trick up his sleeve to circumvent an honest impeachment/removal process. I suspect Pelosi is aware he does, too. And perhaps that explains her choices. Is she a "coward"?
There are two basic positions:
1. The House should vote to impeach as soon as possible and trial in the Senate should start as soon as possible for various reasons of varying degrees of respectability and veracity, including 'the only other alternative is to do nothing'.
2. The House should not take impeachment off the table, but should concentrate on first informing the public about wrongdoing by Trump and his administration, including coordination with Russia, being compromised by Russia and other foreign nations, emolument-clause violations, security clearance procedure violations, constitutional violations and so on.
Can I absolutely say with certainty that Mitch McConnell wouldn't allow a vote? Maybe not, but I can guarantee you that, as of this moment, he wouldn't allow anything approaching a legitimate trial to take place in the senate should impeachment fall into his lap.
Trump is damaged pretty badly in the House but McConnell is still relatively confident that he can keep the Senate, then there will be no trial. He'll sweep it under the rug and move on. If he believes that Trump is so radioactive that he might lose the Senate, then I could see him allowing a trial, but right now, I just don't see it. As long as McConnell is confident of keeping the Senate, he will protect Trump, either with a sham "trial" or no trial at all.
McConnell will protect Trump so long as protecting Trump protects McConnell