Quote from their Best Price Guarantee page:
Request to Add or Change an Added Value Offer
Celebrity will 1) apply an Added Value Offer to booking and 2) go to prevailing eligible cruise fare
NOTE: If either the new cruise fare or Added Value Offer is not combinable with any promotion associated with the existing booking, or changes are being made outside of promotional booking window, the existing promotion will be removed from the booking. No refund or exchange will be given on a promotion offer (added value)
NOTE: an Added Value Offer refers to an amenity added to your booking, such as an onboard credit, specialty dining, shore excursion, etc.
To me, this means that any OBC you got from your initial booking (the "existing promotion") would be deleted, along with any other promotions that were included in that booking, as you are now booking under the new terms. Would it still be a total savings to rebook? If yes, I still think you should be able to.