Ok, so the consensus seems to be that mahogany is fine for a headless neck.
(The reason the question even occured to me was because of something I read on the Kubicki site,
Kubicki.com... note about halfway down the page, in the section "The Laminated Neck.")
Next question about making a headless... can I simply use a Floyd Rose locking nut to lock the strings at the nut? I.e. no specialized headpiece. I saw something similar on an eBay auction, here's the link to the pertinent photo: Headless, locking nut
My plan is to include a small headstock for aesthetic purposes; also, I plan to have Warmoth build the neck. This way, I can simply have them build their standard neck, with a Floyd Rose nut installed, and simply a smaller headstock. Voila, a "headless" neck from Warmoth. Please shoot holes in this plan if you can, I want to know now if it's not feasible, rather than after I've ordered parts.
PS Another advantage I'd see of using a Floyd locking nut is that I can use a wider nut. The two headpieces I've seen (the ABM and Steinberger) are I believe both 1 5/8" wide at the nut... I prefer a wider nut, and plan to order the 1 3/4" wide Floyd locking nut.