If it's the type that can be charged as a credit card, yes. But keep in mind that most debit cards have a daily spending limit that may be lower than your final cruise payment.
My debit card has a $800 a day limit and I've had to work around that when paying for our cruise with my debit card. I usually make a payment a day or one payment on a weekend. With my bank it took a few days for my payments to DCL to actually clear my account when using the debit card.
Really?? I have never heard of a spending limit on a debit card. Mine has a limit on ATM withdrawals in a day but I always figured the spending limit was the cash in the account.