I actually would seriously doubt that it does.
Either way, including a copyright notice is an extremely-cheap hedge, with little or no appreciable downside risk; if it deters even one copier, it has justified its close-to-epsilon cost.
Except, as I pointed out, it has serious downside risk. If you do it wrong, you are heavily penalized by law. If you do it right, you get some vague and possibly zero benefit.
For U.S. works created after the Berne Convention went into effect in 1989, that won't be the case. Consider the possibilities under 17 U.S.C. 406(b):
1. If you use too-early a date in the copyright notice, you lose that many years of protection. If it's just a year or two, or even 10 years, that's almost literally rounding error compared to the term of copyright.
2. If you use a year that's one year too late (e.g., 2016 for a 2015-published work), you're fine.
3. If you use a date that's more than one year too late (e.g., 2018 for a 2015-published work), it's the same as publishing with no notice. But because it's a post-Berne work, you don't need a copyright notice. So you don't care.
So for post-Berne works, there seems to be almost literally zero downside to including a copyright notice of some kind. Even just the word "Copyright XYZ Inc." with no date would give you some deterrent effect, even if it turned out to have no legal significance. Am I missing something here?