Or do they spawn with it already equipped?

In other words, if I have a script that changes some Actor Values when an actor equips an item, will they be changed when the character is spawned, or would the character have to unequip and reequip the armor?

This would be so much easier if the GECK had inheritance settings...

The character will equip whatever armor you specify in the GECK. If that armor has a buff to it, then the buff will be applied if the character is wearing it.

You could use a Perk to apply the buff, then the character could have the Perk applied or removed based on what is equipped if you want this independent of the equipment.