Andres,
Your message is the first time I've heard anyone discuss this combination...so, green field!
I'm not very familiar with doxygen, so I didn't have a response of the top of my head. I did a quick scan of the documentation and found that Doxygen provides an input filter extension point that let's you run the source files through an external program. This may be a possible hook for tying in Asciidoctor.
I noticed that Doxygen interprets Markdown in documentation text automatically. If we wanted AsciiDoc support at that level, it would likely mean writing a C processor for AsciiDoc. There's probably a C processor for AsciiDoc out there somewhere that can handle the most basic stuff...but obviously nothing like using Asciidoctor.
I'd explore the input filter route and see if that can be done in a reasonable amount of time.