Yes, you can purchase WiFi plans only once your are onboard. As getmetros said, for the past few years there has been an offer of 50 mb at no cost if you log onto the purchase site on the first night. Then, when that is used up, you can decide which plan, if any, to purchase.
Note that the onboard Disney Cruise app, which provides information about ship activities and allows texting between passengers, does not require a WiFi purchase. Also, note that many Apply iOS users have reported been able to text other iOS users (even those not on the ship) without a WiFi package.
The internet offered on board we found to be very slow and usually more hassle than it is worth, especially for the price point.
In May 2019, they were testing free texting through iOS devices through iMessage on the Fantasy. I'm not sure if they are still doing this or if it expanded to other ships. We were on both the Fantasy and Dream last year and were able to text those not onboard who had iMessage.
WiFi plans
in Disney Cruise Line
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The internet offered on board we found to be very slow and usually more hassle than it is worth, especially for the price point.
In May 2019, they were testing free texting through iOS devices through iMessage on the Fantasy. I'm not sure if they are still doing this or if it expanded to other ships. We were on both the Fantasy and Dream last year and were able to text those not onboard who had iMessage.