If you are outside your final payment, the price drop will be honored. This is because you could possibly "cancel" and then rebook if they wouldn't give you the price...and that is just too much of a hassle for everybody.
Inside the final payment, if the prices drops, whether you will get anything is anybody's guess. Sometimes, if your travel agent pushes hard enough, you'll get a shipboard credit. Or if you have cruised a number of times, you may get the reduction because of loyalty. Other times, they will just not give you the reduction if the promotion says "new bookings only". If you do get a price reduction after final payment and with a "new booking" promotion, consider yourself lucky and be thankful. But, by no means should you automatically expect it.