Is it helpful for a mom to take the time to put her child in a car, drive around, and get him to fall asleep?

Sometimes... ...This is the only thing that will work!
I wouldn't start. Various studies show that any involved ritual to induce sleep; rocking, feeding, riding around, etc. increase subsequent sleep disorders for the first 4 years by 400%. Make the sleeping area comforting, with some light and sound with you reading in the distance.The kid can settle and resettle later in the night after you are gone. .