No.
What is true is that one of the big ammunition companies recently put out a letter to the public addressing the ammo shortage. They DO state that they will continue to fulfill government orders first and will not divert that ammo to cover commercial shortages.
They are telling people to expect delays and to see a price hike of 5-10% on ammunition, but ammo will be coming and they are looking to hire more people to get it out the door faster.
If people stop panic buying, this could turn out to be a dip rather than a shortage. Distributors and stores have been carrying X amount for a long time. All of a sudden demand shoots up. Even if it only happens for one week, it takes time for the entire supply line to respond.
Kind of like the "beer game" that's used in business classes.