This same question was just answered a few weeks ago on Disney's mom panel site, they said no. I've never wanted to get popcorn on the ship, seems like any time we've gone by Preludes the popcorn always smells burnt.
Experiences posted here say the answer is yes. We purchased a popcorn bucket several cruises ago. It says "Disney Parks" on the bucket. We've brought it back for every cruise since then, and they have refilled it for the reduced refill price with no question.
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