CC3 (and previous versions like CC2 and CC2 Pro) are built from FastCAD licensed from Evolution Computing. If you look at File -> Save As in CC3 (this should be the same for CC2 as well), you will see on the Save As... dialog box the Save As Type drop down box. On that list you will see that you can save from CC3 AutoCAD DWG and AutoCAD DXF files.

DXF files are supported in Adobe Illustrator (according to this link at Wikipedia).

Other than CC3, I'm not a CAD user, so I don't know that much about the file formats other than what I've read. But in theory, you should be able to export vector symbols from CC3 as DXF files and open them in Illustrator. I don't use Illustrator either though.

There's more at CC3 Online Help here:
http://www.profantasy.com/cchelp/hlp_def_dxf.htm
http://www.profantasy.com/cchelp/cc3...md_acadopt.htm

Hopefully this will give you a starting point. If it works, be sure to report back!