From a licensee:
The issue is that under certain edge conditions I am experiencing Anim Notifies not being executed on our Dedicated Server ( it is an off case, so they typically do work, there are not issues with character not being rendered/ticked etc. ). Upon debugging the AnimInstance, I see that the Anim Notifies are indeed queued, but then under certain conditions they are cleared out before they can be Dispatched. It seems to be an artifact of UCharacterMovementComponent::ServerMove() / MoveAutonomous() and how the ticks are done in the AnimInstance/MontageInstance classes.
There's no existing public thread on this issue, so head over to Questions & Answers just mention UE-216156 in the post.