The customer cannot violate Regulation E by requesting that you not send statements. The bank will violate Regulation E if it fails to make the required periodic statement available.
That means that, if you print hardcopy statements, you must either send it to the customer or follow customer instructions to hold the statement. Please note that there are problems inherent in permitted "hold" statements, unless you have strict controls.
You also have the option, perhaps, of conforming to §205.17 and providing e-statements. These can either be pushed to the customer or delivered in a pull environment (generally preferred).
But you must prepare and make available a statement.
John S. Burnett
Fighting for Compliance since 1976
Bankers' Threads User #8