When the impeachment of Donald Trump became a likely event in September, it became fashionable to speculate how Trump's re-election fortunes might be affected: would the process hurt Trump by generating damaging disclosures and negative publicity, or would he benefit from a popular backlash and highly-mobilized Republican base? I suggested at the time that impeachment wasn't likely to matter much in the 2020 general election, and the evidence so far is consistent with that expectation. Trump's job approval rating has barely moved since the beginning of the impeachment push—or, really, since the end of the government shutdown last winter.
A more unsettled question is whether impeachment has had, or will have, any effect on the Democratic primary race. Since all serious Democratic contenders agree that Trump's impeachment is merited, any effect would need to be more indirect—but there are three plausible ways it could occur. First, the connection of Joe Biden and his son Hunter to the Ukraine affair could be expected to influence Democratic voters' perceptions of Biden: either positively (as Democrats might rally around Biden in partisan solidarity or view him as Trump's personally most-feared opponent) or negatively (if they became troubled by Hunter Biden's role in the story and began to worry that it would dent his father's electability). Second, the attention that the news media and American public would inevitably divert to impeachment could deprive Democratic candidates of valuable popular visibility during the key months preceding the first nomination events in Iowa and New Hampshire. Third, the fact that so many of the Democratic candidates in 2020 are members of the Senate means that they will be forced to choose between attending the trial early next year (assuming that articles of impeachment are indeed approved by the House, as seems certain) and joining their rivals on the campaign trail.
On the first question, it's not yet clear whether Biden's popularity has changed much since the Ukraine story broke. The Economist's polling analysis indicates that Biden's share of support in national polls has remained steady since the end of the summer, although his lead has fluctuated due to the rise and subsequent decline of Elizabeth Warren. But in Iowa, Biden does seem to be losing some strength: first Warren and more recently Pete Buttigieg have pulled ahead of him in the RealClearPolitics polling average since the end of September. Of course, it's possible—even probable—that this decline has little to do with impeachment. But, at the least, there is no sign of a pro-Biden rally phenomenon among Democratic voters.
The second question is harder to answer, since it requires considering a counterfactual timeline where impeachment does not occur. In that scenario, it's likely that the Democratic contest would be a more prominent national story, which might in turn have made it a bit easier for candidates who aren't already well-known to have gained some upward momentum. The surprising withdrawal of Kamala Harris earlier this week underlines the unusual lack of volatility in the race so far—and, in particular, the inability of anyone in the large field of contenders other than Biden, Warren, Buttigieg, and Bernie Sanders to consistently attract significant support from Democratic voters.
Normally, a contested presidential nomination is the top political story in the fall before an election year. But we are not in normal times. It's a safe bet that Trump would have continued to dominate news coverage of politics, as he has ever since he began his campaign in the summer of 2015, whether or not he was facing an impeachment inquiry. Any candidate needing a late surge—Cory Booker, Amy Klobuchar, Julian Castro—will find it hard to attract the necessary media hype as Congress moves toward a well-publicized impeachment vote and probable trial over the remaining weeks before Iowa and New Hampshire. But there's also no particular reason to believe that such a surge would have happened absent impeachment, given Trump's continued public ubiquity and how little success these candidates have found so far.
The final question pertains to events that have yet to occur. Mitch McConnell and the Republican Senate leadership will assuredly not schedule a potential impeachment trial in order to maximize the convenience of the multiple Democratic senators who remain active presidential candidates. But it's hard to see how much mischief McConnell could cause—will these senators indeed feel compelled to attend every impeachment session in person?—and there isn't much political logic to Republicans' intentionally trying to disadvantage Warren and Sanders, whom conventional wisdom suggests the GOP would rather face in 2020 than Biden or Buttigieg. Sitting senators will also have the unique opportunity to make stem-winding floor speeches on behalf of conviction that will undoubtedly receive extensive publicity and attract considerable attention from Democratic voters.
All in all, it's not especially likely that impeachment will be a decisive factor in the Democratic presidential race. Nomination politics can be full of complications and unpredictability, so conclusions must be made cautiously and provisionally. But observers looking for the political consequences of impeachment should probably start their search elsewhere.