It could be pretty close. There's no way of knowing when you DCL bus will pick up until the night before embarkation. Busses pick up any where from 10:45-12:30 normally, but can be as late as 1:30. It takes about an hour to get to the port from WDW.
It seems to me that the spa is never very crowded on the boarding afternoon. Why not just wait till you're on board and see if they can fit you in the spa then. There won't be any way to know what the departure time from the Polynesian is until the night before the cruise.
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