Can't help you with the spa, but Guest Services is available 24 hours/day. I was there one night at 1:30 AM, and was there every morning before 5 AM, chatting with Baxter.
GET UP TO A $1000 SHIPBOARD CREDIT AND AN EXCLUSIVE GIFT!
If you make your Disney Cruise Line reservation with Dreams Unlimited Travel you’ll receive these incredible shipboard credits to spend on your cruise!