Well, if POTUS felt persecuted he could fire the prosecutor... Sure, impeachment would likely follow e.g.: Richard Nixon and then etc... just saying. Impeachment is a political procedure, not legal. POTUS could be impeached for his hair e.g.: Maxine Waters style or color.
This is why MSM constantly tries to separate Trump from his base. A while back I saw some MSM news moll attacking an evangelical in intvu for continuing to support Trump in light of Stormy Daniels. Ridiculous from those who defended Bill Clintooon, Ted Kennedy, et al.
Trumps 'base' seems to realize this. Well, we will see.
The legal action persists in Court.
Still, the question is academic. Neither Mueller not any federal prosecutor would indict a sitting president. Too messy. Pluse there is a Solicitor General Opinon, A Sitting President's Amenability to Indictment and Criminal Prosecution
The indictment or cnminal prosecution of a sitting President would unconstitutionally undermine the capacity of the executive branch to perform its constitutionally assigned functions.
Not that this could not be amended or reversed, but until that happens, this opinion is the "lay of the land" for Mueller and the rest of the DOJ.
Impeachment first or second, no doubt the action would be a distraction.