Changed behaviour gets noticed. It disrupts the status quo. It can be a positive diffentiator. A lot of marketing is based upon claims that we do things differently and this is better for you.
But changed behaviour can also occur for defensive reasons and that also gets noticed (as Facebook have been reminded this week).
It is noticed when a credit card company starts sending monthly bills about two weeks later than before. It is then noticed that this wasn't due to the holiday season postal glut but was apparently a policy change.
The changed behaviour has certainly got the customer's attention, but that customer is now wondering if they're trying to increase the chance of his making a late payment. Customers don't like sneakiness - peceived or actual. They notice it. Don't do it.