Wow. That’s an interesting take.
Never thought of that.
But, to take it to an extreme, what if he committed murder. Impeachment would remove him from office, but it would not address the criminal act. That would take a follow up indictment a prosecution.
Impeachment is a political act. Criminal courts are for criminal acts.
According to the Constitution criminal acts in office are covered by Impeachment. Criminal courts are for civil offenses and cannot be charged for ‘crimes’ which are enumerated in the constitution. Charging again is double jeopardy.