We won't know if a ban on reporting election polls will increase turnout until we try.
Apophenia: Put an End to Reporting on Election Polls, 2016-Nov-10 by danah boyd
...there’s a more insidious problem with the polling data that is often unacknowledged. Everyone and their mother wants to collect data from the public. And the public is tired of being asked, which they perceive as being nagged. In swing states, registered voters were overwhelmed with calls from real pollsters, fake pollsters, political campaigns, fundraising groups, special interest groups, and their neighbors. We know that people often lie to pollsters (confirmation bias), but when people don’t trust information collection processes, normal respondent bias becomes downright deceptive. You cannot collect reasonable data when the public doesn’t believe in the data collection project And political pollsters have pretty much killed off their ability to do reasonable polling because they’ve undermined trust. It’s like what happens when you plant the same crop over and over again until the land can no longer sustain that crop.
Election polling is dead, and we need to accept that.