If the price change carries the caveat "new bookings only", which most close in price drops do, the answer generally is no. There are some exceptions. It never hurts to ask your t/a to check. One possibility is no price reduction but an upgrade in cabin category. There is no "black and white" answer to your question. Check it out with your t/a.
when the price dropped on my cruise 30 days out I found it easier to get on on board credit then wait for a check to be sent out I was going to spend it on the cruise ship so why not the credit......Bobbi