If by 'instant' you mean will it show up in your account in some fashion, probably not. But you can certainly trade in your old iPhone now and then whatever the adjustments are to pay off that balance and apply the difference to your new phone, etc., will all get worked out and probably won't be fully visible to you until you get your first monthly bill with the new phone.
if you have a local AT&T store then I am sure they can take care of all of this for you, assuming that they have the new phone in stock that you want to get.