My dissertation (oh the joys) partially looked at the age gap in likelihood to vote. But essential likelihood to vote is the chance your vote will make a difference, times the benefits of voting for your preferred candidate, plus the perceived benefit of voting as an act, minus the costs of voting.
So yea lowering the drinking age might encourage a few to vote, but that being said young people in general don't really perceive voting to be a duty like many old people do. The youth vote does tend to pick up when there's radical political change, but the chances of that happening soon is pretty slim in most western nations.
You've got to be pretty desperate as a major party to try and garner the youth vote to gain electoral success.