My son is allergic to dairy and eggs (first time he had anaphylaxis was at about 8 months due to a tiny bit of yogurt). I know the whole plain meat thing! When he was a baby, and doing finger food, at McDonald's (yes, I know, mom of the year here but this is the real world and I'm busy sometimes, LOL) he'd eat the plain burger that I'd break up!
Disney is amazing with food allergies! I mean amazing! That is one reason we kept coming back, year after year. First time at Boma for dinner, he was 5 or 6 at the time. Chef walked us through the buffet, explaining what dishes were safe (by the way, cast members are constantly changing out serving utensils at Disney). Then he offered to make whatever my son wanted. Salmon on sugar cane skewers! My son was thrilled!
Counter service is good, often excellent. One trip, just me and the kids (he's 6 there), at DAK Restaurantasaurus, back then they had chicken nuggets for the kids meal. I asked for the plain hot dog, no bun, instead. They subbed it for a kids meal, no extra charge. The receipt even had hand written by the manager "change gloves". The next day we went back, same manager remembered not only us, but what he wanted! How's that? Back then, once you said, "allergy", they had to call a manager over to help you at counter service.
Now, they have books with ingredients to help you. At some kiosks they may have to call someone on their phone.
In my opinion, though, I don't know if I'd add the dining plan over just paying out of pocket. There are many dairy-free options. Gluten can be avoided, but it's a slight bit harder. Sugar - that one is hard. I'm guessing it's that they feel it helps some sort of autism, not an allergy? Allergy is only protein. With the dining plan, there are not many "snack credits" that are sugar free (or gluten free), so it may be less expensive to just order what works and pay.
Definitely, at counter service, you could order the burger without the bun (or hot dog as well - back when they used Interstate Brands buns that contain whey, my son couldn't eat buns at Disney).
I just think they may end up wasting money on the plan, and do better OOP.