So this is a weird one.

Steps to reproduce:
1. Place a repreating Command Block
2. Input command: /execute @e[type=Arrow] ~ ~ ~
/summon Fireball ~ ~ ~ {direction:[0.0,0.0,0.0]
3. Power the Command block
4. Place a dispenser
5. Put arrow in the dispenser
6. Power the Dispenser.
Observe that arrow DOES hit the Fireball, since hit sound can be heard, and the arrow disappears.

Same goes with arrows summoned by commands/command blocks.
Follow steps 1-3.
4. Input into the chat /summon Arrow ~ ~ ~

The hit sound can be heard again, the arrow disappears too upon hitting the spawned Fireball.