Some do, sure. But definitely not all of them.
In 2022, only 4 of the 10 rookies taken after #11 before the third round had >500 yards as rookies. 5 of them had less than 300 yards.
In 2021, 7 rookies were drafted after #10 before the third round. Only 2 of them had >500 yards as rookies.
You are just asking for another season watching Gabe Davis flub the ball.