That would be a LOT of fun but I am afraid the answer is no. You can, however, take advantage of their "Wine and Dine" program. Purchase the package and receive a different bottle of wine with dinner every night. It's a discounted amount off regular prices but it is still not all you can drink. Some excursions offer all you can drink in the price of the tour. That would be your best option.
As far as monitoring the cost, you will receive a receipt with every drink that you purchase with a 15% gratuity already added in. You can check the balance of your sea pass (and even get a printout) whenever you wish.