Reducing the AP to reflect a price drop does not affect the actual order, so does not affect lead times. It’s a less than 5 minute job for the salesperson on the Motability system. The actual order is different and on an entirely different system as it’s between the dealer and manufacturer and unaffected by the AP.
With our last car the BMW dealer made the change without me even asking. It was only £150 but their view was “that £150 is better in your pocket than Motability’s”. With our current car I got the Hyundai dealer to agree up front that if the AP was reduced they would adjust it and they were more than happy.
The money that the dealer makes from the sale is completely unaffected by the AP. Although Motability don’t like dealers adjusting APs, most decent ones will do it.