Like other personal protection items, a bulletproof backpack insert is rated at different levels and will protect you against different calibers. The inserts are rated the same as body armor, ie.:
Level III, and
However, most backpacks use soft Level II and Level IIIA aramid inserts as they are lightweight and can stop most handgun calibers, which are the most common and likely weapons a school shooter will use.
So, the final answer is yes, bulletproof backpacks work as well as any other bulletproof vest, and -provided the right panels is inserted – will protect the wearer from almost every type of pistol round.