When I issue a full refund does the inventory go back into my inventory automatically?
No you need to follow the steps of the order cancelation process.
As Brickwilbo writes, you have to cancel the order in order for the inventory
to go back. I think there's a good reason for this - you might refund the
order for a variety of reasons, including the order getting lost in the mail.
You wouldn't want that going back to your inventory.
Canada, British Columbia
Netherlands, Gelderland
USA, New Jersey