Again this varies from bank to bank.
I know of some banks who book the cars in advance and when you approach them they ask you if you want early delivery from the bank's stock which will cost you 10% more than the actual price plus the regular markup and installment plan or do you want the bank to book a car now and would wait for it's delivery.
So let's say a car costs 3 million ex showroom and 10% per year so in the first case the bank will charge you 3.3 mil plus the 10% per year and you will get the car in less than a week. (Normally 2-3 days)
In second case the car price will be 3.0 million plus 10% per year but you might have to wait 2-3 months (regular waiting time) for delivery.
What you are mentioning is the 3rd procedure where the Bank tells the manufacturer that we are a big customer so we need expedited delivery after regular booking. In that case the customer gets the car in approximately half the regular waiting time.