Here is what I believe is the controlling Supreme Court case:
https://supreme.justia.com/cases/federal/us/549/225/
The answer is yes, he can do this, at least for now.
If the statements made by Trump that form the basis of the lawsuit were made in the course of his official duties as President, he is absolutely immune. The statute is designed to protect federal employees from the cost and burden of having to defend lawsuits arising out of actions performed in the scope of their duties. it doesn't matter if Barr is full of crap. His certification that Trump made the statement in the course of performing his duties is conclusive as to removal of the case from the state court to federal court. The case can never be remanded back to the state court. The case will be presumed to be brought against the United States and not Trump personally unless and until the federal District Court determines that the making the statements were outside Trump's official duties. If the District court so rules, that can be appealed all the way to the Supreme Court. Unless that ruling is upheld, the Justice Department will continue to defend, the case will not be against Trump individually, and Ms. Carroll will have no right to a jury trial.
The delay is real and substantial. There is zero chance that any discovery will be conducted for at least a year. More like two or more. If it had stayed in the state court, discovery could proceed at any time.
This is what Trump does. The statute is a good thing, as it prevents the filing of lawsuits in bad faith that would financially ruin federal employees due to the cost of defense. But, like everything else in a system of government, it assumes a basic level of good faith by those in power. Barr knows he's full of crap, but he also knows the federal court system will not tell him he's full of crap until long after the election. This is the archtypical example of "why we can't have nice things."
“The ideal subject of totalitarian rule is not the convinced Nazi or the dedicated communist, but people for whom the distinction between fact and fiction, true and false, no longer exists.”
― Hannah Arendt, The Origins of Totalitarianism, 1951