Trumpers are saying no, based on a Nixon era policy...
But you might remember that Clinton was forced to testify in a CIVIL SUIT regarding an event that occurred years before he was elected.
That sets the bar considerably LOWER than what we are discussing here
I'm not sure about the Slick analogy. I think we'd both agree that the legal process and constitution were misused in impeaching a man for lying about extramarital sex.
But, unless Justice Kavenaugh would secure a majority to change things, it seems clear to me that a President must comply with legal process to turn over documents or answer questions in legal matters. But the courts should not allow any questioning that interferes with executive privilege.
The question is whether a potus can be indicted. Federal judges can be indicted while in office, and even tried while in office.
And indictments and trials are different animals. Non-federal prosecutors and AG's have pretty much unfettered discretion to indict. A county DA for example doesn't need anyone's approval. A governor can't keep a state AG from indicting. However, I think US attorneys have to have approval from higher up in the DOJ to indict.
A trial is more difficult. A potus could ask a court to toss or delay trial on any indictment.