The Democrats are going to put HUGE pressure on Rosenstein to stay on board and continue with obstruction, or force the President to fire him. Since it is unlikely that the President will fire him, don't count on Rosenstein going anywhere. After the Dems work on him, his resignation is out of the question.
Rosentein leaving office voluntarily will cause the whole house of cards to collapse, the whole chain of dominoes to tumble over, flop, flop, flop, flop. Once Rosenstein is voluntarily out it will be a massacre.