lakerman, sure, you can use Illustrator - it allows you to od everything Inkscape does (and probably more, I guess). Inkscape is generally recommended mostly because it's free and good enough.
However, there was a thread a few days ago here from someody using Illustrator, asking for help - http://warlight.net/Forum/Thread.aspx?ThreadID=2697
- he couldn't find the function to assign ids to objects (for examples, Territory_N to designate territories). Since not a lot of people use it for Warlight, you might have trouble finding help if you ever need it, too.