There's really no need to use layer comps in Illustrator. Illustrator and Fireworks and InDesign support symbols. So you can simply save your different visual components as symbols and mix and match them in different artboards without increasing disk usage.
If you're using comps to mockup different UI states or pages, then just:
- Create a base template containing common header/footer/BG elements.
- Create a symbol library of all your UI components (including the header/footer/BG elements).
- Mock up different pages in different artboards.
If you're using comps to mockup different design variations, then just duplicate artboards and create/duplicate symbols as you go. You can have 20 different versions of a design and still only increase the file size by 50~100% if most of the designs use shared symbols. Though to get the best effect, you'll want to separate simple fills from outlines so that you can re-use an outline symbol and just drop in different color fills to get different variations.
You'll need to adapt your workflow slightly, but it shouldn't be that difficult.