The short answer is no he can have a knee on the ground and pick up a bad snap and advance per the rules below.
Here is the long answer:
NFHS Rulebook - Rule 4, Section 2, Article 2 (Exceptions):
The ball remains alive if, at the snap, a place holder with his knee(s) on the ground and with a teammate in kicking position catches or recovers a snap while his knee(s) is on the ground and places the ball for a kick, or if he rises to advance, hand, kick or pass.
Also, The ball remains alive if, at the snap, a place holder with his knee(s) on the ground and with a teammate in kicking position rises and catches or recovers an errant snap and immediately returns his knee(s) to the ground and places the ball for a kick OR again rises to advance, hand, kick or pass.
NOTE: The ball becomes dead if the place-kick holder muffs the snap or fumbles and recovers after his knees have been off the ground and he then touches the ground with other than hand or foot while in possession of the ball.
You might notice above that the knee(s) on the ground is only for putting the ball down for a kick. If he is going to do anything else with the ball he needs to rise up (knee off the ground)
Let me know if you have any other questions.