No, not like that, at least not yet.
Rather, odds are that Trump will have to answer questions in a deposition:
A New York State judge ruled on Tuesday that a defamation lawsuit brought by a woman who has said President Trump made unwanted sexual advances could go forward, raising the possibility of a public airing of other allegations of sexual misconduct against the president.
The decision by Justice Jennifer Schecter of State Supreme Court in Manhattan paved the way for lawyers to seek depositions from several women who accused Mr. Trump of sexual harassment before he was elected and to subpoena Trump campaign records related to his female accusers.
Justice Schecter rejected Mr. Trump’s argument that a state court has no jurisdiction over a sitting president. She cited a United States Supreme Court ruling that allowed Paula Jones to bring a sexual harassment suit against President Bill Clinton.
Actually, the issue of whether the Paula Jones precedent should apply with full force in state court is not frivolous at all. I can imagine reasons why a court might hold that there is too much risk of interference with the President’s, ahem, affairs to allow just any court to make demands on his time. Then again, I can think of even more arguments why the state courts should be allowed to proceed — if only that surely a sitting President could get an injunction from a federal court if the state court were to misbehave in some way.