“Some of you will succumb and some of you won't, and my sending this warning won't alter those proportions.”

Of course sending the warning will have an effect because it becomes part of the conditioning of the people who read it! They don’t get to choose how they will be affected by it, but it will certainly have an effect. To say that a person has no free will is not to say that they are not affected by their environment.

Compared to not sending it? Of course – but that's a counterfactual. The present leads to the future, where this message is sent; the act of sending the message did not alter the past.

Compatibilism isn't a new invention, and Chiang ought to have heard of it, but it isn't mentioned at all in the story.