When you upgrade to a new category on the same cruise, you will pay the same fare as it was the date you initially booked. I don't watch concierge rates much, but I don't believe they increase as quickly as the regular fares. Just be aware that once you upgrade to concierge, the deposit becomes non-refundable, even if you later decide to downgrade. Also, if you are using an OBB or placeholder, there is no discount for concierge.
Enjoy your cruise!