Yes you really should wash the newborn clothes before the baby wears them even if they're new newborn clothes as there could be some leftover dye in the clothes that could transfer to the babies skin.
Also if the newborn clothes are bought used they should also be washed prior to your baby wearing them because your newborn babies skin is very sensitive and if anything that shouldn't come into contact with the babies skin does come into contact it could cause rashes or anything else that could be bad.
So wash the newborn clothes and then put them away separately in a dresser drawer in the newborns room or in your room.
I would also wash the newborn clothes separately from your other others clothes and use a laundry detergent that is best for newborns sensitive skin.