The ability to e-mail customer statements directly to customers is a new (and long overdue) feature of the new 2017 version of NAV. But it’s a little quirky.
When I first ran it, by selecting E-mail as “Report Output” in the Customer Statements screen, it did, well, absolutely nothing! No error message, nothing.
I discovered that it only works if you specify an e-mail address for the customer under “Documents Layouts”, which you can get to via the customer card. Fill it in as below: