Load up the AVD with supply and it will work. I done the same thing in Wienie Roasting with French Frigate Shoals.
In the stock AE scenarios, the AVDs have zero bulk capacity, which means they cannot be loaded with supply. It's a pain to set up a forward seaplane base when I need to use an APD to drop off supplies on my targeted island. Otherwise, when a plane is down for maintenance, it stays down without supplies.
OK, this needs tweaking. How much supply did they bring?
Nosing around, I note the APDs converted from 4-stackers carried 144 troops, but no cargo, which suggests a couple hundred tons of supply at most. The AVDs had their forward boiler room converted to avgas fuel tanks. The purpose-built ones later in the war had 80,000 gallons of avgas, or about 250 tons (of supply), so the conversions probably had about 200 tons of supply.
The problem exists for all AV ships. Without research, I've been using 10% of tonnage for AV and Barnegat AVP, 5% tonnage for AVD and Bird AVP, and 7% tonnage for Langley (only to keep it in line with the AV ships). That's roughly 800 (game) supply for AV and Langley, 120 for Barnegat AVP, and 70 for AVD and Bird AVP.
OK. With a little research (looking in Conway's), AV ships were designed to handle two squadrons (for several months) while Barnegat-class were designed for one squadron (duration is uncertain). Avgas for Barnegat-class is 80,000gal, Currituck is 278,000gal, Curtiss is 269,000gal, Pocomoke is 291,000gal, and I'm not certain about the other large AV ships but they will be 312,000gal or less.
Few things are harder to put up with than the annoyance of a good example. -- Pudd'nhead Wilson