can I use bun legs on a huge kitchen island?

What's a bun leg

Is the island a cabinet or a table... you need to make sure that the "apron" of a table is beefy enough to not allow sagging between the legs.

-Steve

I don't understand the diagram, but if the island is a solid box like a cabinet carcase, then you support it on a recessed (out of sight) base of toe kicks and then trim it out with bun feet and split-dowel "legs." The bun feet do not support the unit, and the "legs" are just molding. Rockler has a bunch of examples under "wood products." I hope I understood your question.

I'm not sure what CAD program you're using, but the results are more than a little odd. What are those boxes and what's with woodwork dimensioning to 4 decimal places?

As someone else posted, it's better to have a conventionally supported cabinet with decorative elements applied. Cleaning under the island would be a total bitch.

BTW, you are planning to have some electrical receptacles on that island, aren't you?

Yes there will be electrical devices. This is a totally custom job. There will be 2 square cabinets on the flat side, the curved side is a custom wall my contractor will build.