There is research on postal voting. In some jurisdictions, I think Sweden, most people vote long before the election takes place. The hope was that postal voting would make it easier to vote, and therefore would raise turnout. Most of the research with which I am familiar says that what happens is that those people who would vote anyway find it easier to vote, and those people who wouldn't vote anyway don't vote just because they can vote by post. It facilitates the regular voter, not someone who's turned off from the system.
On July 26th, 2016. See this statement in context.