Yes. Both Disney Gift Cards and Disney Visa Redemption Cards (I assume that's what you mean by "rewards cards") can be applied to your onboard account. You can either call in advance to do this or do it at Guest Services onboard. During online check-in, you can also indicate your Disney Visa card (the actual credit card) to be used for onboard expenses as well in case your gift cards and/or redemption card doesn't cover it all.
Enjoy your cruise!