How does a poisoned arrow combine with the spell Conjure Barrage?

A Ranger casts the spell Conjure Barrage:

Conjure Barrage (Instant):You throw a nonmagical weapon or fire a piece of nonmagical ammunition into the air to create a cone of identical weapons that shoot forward and then disappear. Each creature in a 60-foot cone must succeed on a Dexterity saving throw. A creature takes 3d8 damage on a failed save, or half as much damage on a successful one. The damage type is the same as that of the weapon or ammunition used as a component.

For the component, they use a piece of ammunition that has been coated with poison, let’s say Wyvern poison:

Wyvern Poison (Injury). This poison must be harvested from a dead or incapacitated wyvern. A creature subjected to this poison must make a DC 15 Constitution saving throw, taking 24 (7d6) poison damage on a failed save, or half as much damage on a successful one.

Does the target of the spell also incur poison damage from the poison? I am inclined to say yes since, “The damage type is the same as that of the weapon or ammunition used”.