Yes, the Republicans have many seemingly effective talking points that are critical of Hillary Clinton's email scandal and this could sway some voters. In popular discourse it is common to hear people referring to Clinton as dishonest or untrustworthy and this seems to be a widely held concern on behalf of Republicans and Democrats. It is likely that this perception has been bolstered by criticism by party Republicans.
These emails will hurt Hillary to the point that the Republicans will be able to take votes away from her. This is because Mrs. Clinton is on a bad path of already not being trusted to being downgraded to perhaps a total liar. So many democrats already did not want her to win, as could be seen at their convention.
Republicans will not likely be able to gain traction with votes by using the recently released Clinton e-mails that shed light on the relationship by the State Department and the Clinton Foundation. Those who find her untrustworthy are already disinclined to vote for her, and this will not sway any new voters.
More than half of Americans has said they feel Hillary Clinton is untrustworthy. She still leads in the polls because almost the same number of people who feel Clinton is dishonest also feel that Donald Trump is untrustworthy. Both candidates are strongly disliked, but this election is more about their party affiliation.