No study has the final word, but the research is all inconclusive enough to suggest that practical barriers to voting have a fairly small effect on whether people actually vote.
What explains this? MIT political science professor Adam Berinsky
offered one theory at the Stanford Social Innovation Review: “The more significant costs of participation are the cognitive costs of becoming involved with and informed about the political world. … Political interest and engagement, after all, determine to a large extent who votes and who does not.”