While I have the 'discount' field showing and applying as expected both for back end memberships, and on the Contribution page, my testing shows the outcome of a Pay Later is that when as an admin updates the payment to 'completed' there is no indication on the Pending Membership record that the user applied a coupon and it is not recorded as a Code Redeemed for that contact.
I tried both 'update pay later' options ie via Membership and via Contribution.
If i use the Update Payment Status on the membership record it provides the Amount field prefilled with the undiscounted amount and no indication of a coupon being associated with this membership - and if i don't overwrite this it will end up recording the payment incorrectly as being the full amount.
Alternatively if i used the Edit option on the related contribution which shows the discounted amount the person is committing to pay and refers to the discount on the line item - when i set payment to Completed and save, nothing is recorded on the Codes Redeemed for the contact nor the Codes Assigned for the Organisation to which the discount 'belongs'. Am I missing something or is this a 'gap' in the current code?
This was testing on civi 4.6.3 and cividiscount 3.0.