Mobs will not use shields, and the shields themselves are purely visual; they don't block projectiles such as arrows.

Effects on different mobs that have visible held items:

Skeletons and Strays: Use their melee attack (the one they use when holding something other than a bow)

Pillagers and Illusioners: Don't attack (MC-139433)

All other mobs: No difference in behavior

How to reproduce (easily):

1. Summon a mob without any held item that has "CanPickUpLoot" set. Example:

   /summon zombie ~ ~ ~ {CanPickUpLoot:1b}

   2. Throw a shield at the mob, wait for it to pick it up, and shoot an arrow at the mob's shield

          → Notice the arrow going through the shield and hitting the mob, dealing damage to it.