The WSJ Editorial Board thinks not:

Democrats accuse Republicans of suppressing the minority vote with laws to ensure ballot integrity. But then how do they explain record minority turnout last November? If Republicans were trying to stop minorities from voting, their schemes were inept.

For a more sophisticated take on the issue, see Jacob Neilheisel and Rich Horner’s new article in Election Law Journal, “Voter Identification Requirements and Aggregate Turnout in the U.S.: How Campaigns Offset the Costs of Turning Out When Voting Is Made More Difficult.” Here’s the abstract:

In spite of the attention that has been lavished upon the subject in recent years, scholars have found little evidence demonstrating that voter identification laws have a substantial effect (either positive or negative) on aggregate levels of voter turnout. Recent work by Valentino and Neuner (2017) suggests that the disconnect between the predictions of rational choice models of voter turnout that focus on the costs of voting and the observed effects (or lack thereof) of voter ID requirements can be explained with reference to the countervailing influence of mobilization efforts on the part of Democrats. We test this proposition directly in this article using data on the location of Democratic campaign field offices over three presidential election cycles (2004, 2008, and 2012) coupled with information on the spread of voter ID requirements and other policies regulating access to the ballot box. Using a series of difference-in-difference models, we find some support for the notion that campaigns can effectively subsidize the costs of new legal-institutional barriers to the franchise.

In other words, they find some evidence that Democratic voter mobilization effectively countered the effects of voter suppression laws.