I've been told mixed things. Special Diets told me they carry then at HH but the chef at BC/YC I spoke with about a month ago said they don't because the kitchen at HH can not safely make them. The chef said that any allergy tenders will be cooked in the allergy kitchen at the Captain's Grille kitchen but that I can order them at Beaches & Cream if that's where we are. I suspect the ability to order them at HH will depend on the willingness of the CM working there at the moment to go into CG to place the order. If it's a slow time then I suspect they'll be more willing to do so. The chef told me to just place the order at CG as a to go order but I also know that chefs aren't thinking about the price; it kind of bugs me having to pay TS prices when I should be able to get it at a CS location. He also mentioned that I could order them to go from Cape May but no way am I paying for a buffet just to get an order of chicken tenders. It certainly beats walking over to Epcot though.
I plan to write an allergy dining report when I get back. If you watch the disABILITIES! board in a couple weeks, I'll make sure to include info about allergy dining at BC/YC since we'll be eating a lot at our resort.