False.
Quarterback options
On quarterback options, any quarterback who keeps the ball and does not pitch becomes a runner and loses the special protections afforded to passers.
In this example, Chiefs quarterback Patrick Mahomes runs the ball on a speed option on a 4th-and-1 play in week three against the 49ers. He does not pitch the ball and keeps it for the first down instead. 49ers defensive end Cassius Marsh applies the hit, legal in this instance since Mahomes is now a runner under the rules.
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Advance as a runner
When a quarterback drops back to pass, pulls the ball down and tucks it to advance as a runner he no longer has the roughing the passer protections afforded to the quarterback dropping back to pass, even when his path of advance is within the pocket. Any penalty on the quarterback for late hit or hit to the head would fall under the unnecessary roughness criteria.
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