Certain aspects of Project Manager can be automated but I have a hard time envisioning fully automated project management except for simple cases.
Automation is better suited for situations that are highly repeatable.
Certainly, machine learning can be used to compare current situations to prior situations to make decisions but people are better at situations that involve adaptation to change and decision making involving abstract variables.
Some examples that include decision making that weighs long term strategy vs. short term metrics and motivating people.