Looking at this quote, it seems you must stay onsite to purchase/use any of the dining plans:
Who Can Purchase the Dining Plan?
The Basic Magic Your Way Dining Plan can only be purchased as follows:
1. If you are a non-Disney Vacation Club member, you must purchase a Magic Your Way vacation package at a Disney resort for your entire party with at least one day's park admission. The number of days for the Dining Plan will equal the number of nights you have reserved your room on the package. It has nothing to do with the number of days of park admission you have.
2. If you are a Disney Vacation Club member staying at a DVC resort on points, you may purchase the Dining Plan. You must purchase the Dining Plan for everyone in your party. No purchase of park admission is necessary. The number of dining plan days will equal the number of nights of your stay.
3. If you are cruising with the
Disney Cruise Line and have
Disney Cruise Line Land/Sea package.
NOTE: The following resorts do not participate in the dining plan: The Swan, Dolphin, Shades of Green and the Downtown Disney resorts on Hotel Plaza Boulevard, which are not Disney owned or operated.