There is a vigorous academic debate over whether negative advertising depresses or increases voter turnout. I suspect it does both, depressing turnout among moderates and independents while stimulating it at the ideological extremes. In that process, what has changed is the composition of the turnout rather than its overall level.
From the Lau, Sigelman, and Rovner meta-analysis of studies of negative campaigning:
We did find some support for the idea that whereas negative campaigns stimulate partisans to get out and vote, they are more likely to turn independents off on voting; however, too few studies (only nine) were involved in this hypothesis test to achieve the power necessary for conventional levels of statistical significance (t = 1.6, p < .07, one-tailed).
I’m not sure how many further studies distinguishing independents from partisans (or moderates from ideological “extremists”) have been published since the meta-analysis. And there is always the question of how large this two-sided effect really is, if it exists. My guess is that if negative advertising demobilizes the middle but mobilizes the extremes, it does so mainly at the margins.