Not generally.

If your speed is sufficient to overtake without getting the oncoming vehicles in danger of a head-on collision with you, you don't need to downshift. You only need to downshift if you want more acceleration/power and you have to do it quickly. Of course, after downshifting, you do not maintain your current rpm or you'll slow down the vehicle (engine brake), you even need to press down on the accelerator more, to get the power you need to finish the overtake quickly.