I would use "think" in the loosest possible sense, as we're pretty much certain it wasn't. Calabash can't be grown across much of that journey, and there's no archaeological or ethnographic evidence to support it. Additionally, the historic varieties are most closely related to African crops, not Asian varieties (with no evidence of founder effect). Furthermore, the seeds remain viable for years even in salt water, so oceanic transport is completely realistic.

Fun fact though, it's found in the earliest domestication deposits in the Americas, alongside squash.