Re:In a word, no! (Score 1)

The best research that I know of (cited below) suggests that E-voting will only make it easier for habitual voters to keep on voting --- it will not bring new voters into the electoral system. Whether this is because of apathy, or something else, I don't know.

See:
@article{votebymail,
author = {Adam J. Berinsky and Nancy Burns and Michael W. Traugott},
title = {Who Votes by Mail? A Dynamic Model of the Individual-Level Consequences of Voting-by-Mail},
journal = {Public Opinion Quarterly},
year = {2001},
volume = {65},
number = {2},
pages = {178-197},
optnote={Main mechanism by which Vote by Mail increases turnout is retention of habitual
voters rather than mobilizatin of new voters.}
}

In the USA, the best research suggests that non-voting is mainly due to restrictive registration laws --- rather than any particular emotion toward the candidates or political system. That is, people don't vote, because our institutions prevent them from voting --- not necessarily because they don't want to vote [although, clearly, if they wanted to vote very much they could surmount the registration hurdles facing them].

The most comprehensive research on political participation in the USA, that I know of includes:

@book{vsb95,
author = {Sidney Verba and Kay Lehman Schlozman and Henry
Brady},
title = {Voice and Equality: Civic Voluntarism in American
Politics},
publisher = {Harvard University Press},
year = {1995},
address = {Cambridge},
optnote = {}
}

@book{woro80,
author = {Raymond E. Wolfinger and Steven J. Rosenstone},
title = {Who Votes?},
publisher = {Yale University Press},
year = {1980},
address = {New Haven}
}

@book{roha93,
author = {Steven Rosenstone and John Mark Hansen},
title = {Mobilization, Participation and Democracy in America},
publisher = {MacMillan Publishing},
year = {1993},
optaddress = {New York, NY},}