Illustrator and pretty much 99.99% of all programs that aren't font managers simply use the OS's list of installed/active fonts. If they didn't, you'd need to install & activate fonts in 50 different places to accommodate 50 different programs. It would get quite messy.
A professional font manager will however let you organize your fonts either by tagging or grouping into folders. You can then quickly enable/disable a large set of fonts depending on what you need at the moment. Likewise, font managers like Extensis Suitcase can automatically activate fonts that are in your font library when you open a document in Illustrator, Photoshop, etc. And when you close the document, those fonts that were activated will be deactivated again to keep your font list lean.
But there typically isn't a need to use different font lists for different programs. There are very few use cases for this type of setup. If I commonly use Helvetica, Akzidenz-Grotesk, Verlag, Chronicle and Museo, then I'm just as likely to use these fonts in Illustrator as I am to use them in InDesign or LibreOffice.
Likewise, if I have a set of fonts that I'm currently using for a branding project for a client, then in most cases I'm going to want them active for when I design the company logo and product marks in Illustrator as well as when I'm designing brochures and business report templates in InDesign, or slideshow presentations in Impress/PowerPoint, or webpages in Fireworks.
I'm much less likely to have fonts that I only want to use in Illustrator or only want to use in Word. I mean, a good display or body type in one is gonna be a good display/body type in the other.