Unfortunately, unlike zombies, vindicators never spawn with the ability to pick up loot. Perhaps they can spawn with their axe already enchanted.

Can Vindicators wear armor?

Vindicators can wear armor too but that is really overpowered considering their damage so it will only be possible in creative mode. You should also be able to swap the vindicators Axe for something else in creative mode. The same goes for witches but they will not spawn naturally in armor.

Can Vindicators break their axes?

Vindicators are quite the terrifying illagers! They carry an Iron Axe and can break wooden doors, actively looking for villagers to kill. They can only break wooden doors in Normal and Hard mode, however.