Above is correct, there are no actual perks of the Disney Visa card while onboard -- no shopping discounts, etc. If you use your Disney Visa to pay off your onboard account, you will earn reward points towards your next vacation. Or as PP mentions, if the full cruise is paid on the Disney Visa (even if paid in installments) you may qualify for a $50 beverage credit if you aren't booked under a discount offer already.
Enjoy your cruise!