Is there evidence to determine whether a vote reminder app be used effectively to boost turnout?

A quick search brings up a few tests which suggest that voter reminders are effective at increasing turnout of the targeted groups. As J.C. points out in their answer, these attempts used existing tools like SMS message instead of a unique app, as people who go out of their way to download a special voting reminder app are almost certainly going to vote.

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In a 2009 paper Don't Forget to Vote: Text Message Reminders as a Mobilization Tool, political scientists Allison Dale and Arron Strauss suggest that impersonal reminders (such as from a text message) are sufficient to create a statistically significant increase in voting rate:

Text messaging is examined as an example of an impersonal, noticeable communication to potential voters. A nationwide field experiment (n = 8,053) in the 2006 election finds that text message reminders produce a statistically significant 3.0 percentage point increase in the likelihood of voting. While increasing social connectedness has been shown to positively affect voter turnout, the results of this study, in combination with empirical evidence from prior studies, suggest that connectedness is not a necessary condition for a successful mobilization campaign. For certain voters, a noticeable reminder is sufficient to drive them to the polls.

Note: I don't have access to the full text, so my conclusions here are from the Abstract alone

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Vote.org is "the largest 501(c)(3) non-profit, non-partisan voting registration and get out the vote (GOTV) technology platform in America". They carried out studies evaluating their effectiveness:

Over the past two years, we have run a number of large-scale controlled experiments in partnership with the Analyst Institute, Pantheon Analytics, and the Harvard Kennedy School of Government. Read more below

For the 2018 general election, Vote.org conducted SMS voter mobilization programs covering 12,681,951 people of color and unmarried women in 33 states. These programs used “cold” text messaging to registered voters who have no prior relationship to Vote.org

Vote.org’s SMS treatments increased turnout in the 2018 election, generating an average increase in turnout of 0.26 percentage points at a cost per net vote of $85.69 (11.7 net votes/$1000).

The program caused 17,586 people to vote who otherwise would have missed participating in the 2018 General Election.

Vote.org’s SMS messages increased voter turnout among people who had requested a ballot. On average, the treatments generated a 0.21 percentage point increase in turnout at a cost per net vote of $75.14 (13.3 net votes/$1000).

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In terms of practicality, I would think the few people that would download an app for this purpose only would be the type that are already politically involved.

Then maybe we could think of this system embedded in an app already widely used, such as FB or Instagram. I would personally be for such a reminder. Well that seems to already be happening and apparently it works.

Not clear I would favor the segmentation of apps per party. I see it as another instance of trying to resolve things by segmenting and reducing cross-party interaction, something that would not help in my opinion.

Semi-related note: We are used to republicans (alleged?) attempts to reduce turnout, but some research seems to show that republicans in some area would benefit from higher turnout, generally due to disproportionate value of rural areas in terms of delegates!