Yes, you can at the coffee bar just next to Kona. It's a sushi bar later in the day. I think that it has the same Kona blend as Kona. Captain Cook's downstairs serves Nescafé like all of the other counter service restaurants in the resorts.
I love Kona Cafe. It is casual enough to bring the kids and an affordable way to start the day. You get a LOT of food. I also like that there are sweet and savory options, and the coffee is great.