ABD really excels at people with dietary issues. I have a lot of them (although I'm not vegan). I can't eat tomatoes, citrus fruit or green peppers, plus I'm diabetic. And I need to eat a cup of plain yogurt a day (my doctor has me eating it to address a couple of different issues). ABD has been wonderful about arranging alternatives for me at all the included meals. It even came down to, when i did the Alaska ABD and they knew we'd been in some remote locations, the Guides bought yogurt for me and carried it in the cooler they had under the motorcoach so I could have it every day.
One one of my ABD's we had a family that ate gluten free because the daughter had Celiac's disease. Again, every place knew ahead of time to have options for them, and when we made pizza, they had totally cleaned the marble counter we worked on, and they went first with gluten free dough, then we did ours.
We had another person on my Greek trip who was allergic to wine, and the Guides were very vigilant to make sure he knew which dishes had wine so he could avoid them.
All you need to do is let ABD know (or have your TA let ABD know) what your needs are, and they will do all they can to accommodate you.
I'd call ABD and ask them specifically about supporting a vegan diet, but my feeling is, if any company could handle it, it would be ABD. I can't imagine that they haven't had multiple vegans on their trips before.
Sayhello
ETA: This is from the ABD FAQ on their website:
http://www.adventuresbydisney.com/faqs/
Can you accommodate special dietary needs?
Adventures by Disney will make a reasonable effort to accommodate some special dietary needs at no additional charge. Unfortunately, we may not be able to accommodate all special dietary needs requested. Please contact a Vacationista in advance of your departure to advise us of your needs.