While I am a huge Southwest fan, I have never booked one of their vacation packages, so I don't know all of the details about working with them. That being said, the answer to this question is usually no. Dining plans are generally purchased only when booking directly through Disney or a few of the Disney-specific travel agencies. Depending on how the package was booked, your
travel agency may be able to add the dining plan in advance, or they may have to cancel and rebook the package. Most report that it cannot be added upon arrival at the resort or by calling Disney directly.
The real question you need to be asking is whether or not you should buy the dining plan. Which level were you planning to purchase and for what purpose? Most report spending far less paying out of pocket than it would have cost to purchase any of the dining plans. Are you planning on mostly counter-service or lots of pre-scheduled Table Service? The Quick Service plan only saves money when it is free. The Deluxe plan can definitely save if you plan on three big meals per day, but it is WAY too much food for most travelers. The
Disney Dining plan sounds like it will work for most people, but you generally have to purchase the most expensive meals to break even cost-wise. Ordering what you would usually eat is almost always less than then cost of the Disney Dining plan. IF you are okay with not saving money, the upside is that you don't have a huge bill at the end of every meal, so you are encouraged to eat and drink freely throughout the trip, rather than worrying about the ridiculous costs which are rarely justified by the mediocre food. For us, this mentality contributes to the care-free vacation atmosphere.
We have found the best balance is to purchase the Deluxe Dining plan for one of our two rooms. The meal credits can be shared with those not purchasing the dining plan so that we are able to enjoy character dining and signature restaurants without worrying about the cost, but with only one big meal per day we also don't feel like we are constantly planning around meals.