At least used in a political context, I've never seen “flyovee state” (which is mostly, in that context, a conservative stereotype of a liberal pejorative) used to refer to Illinois or the Midwest states to its east, only those to its west and the Western States not on the Pacific Coast.

Flyover states are what you fly over on the way from Boston/New York/DC to Seattle/LA/SF. It's anything not near the Atlantic or Pacific coast, where the stereotypical maps say "HERE BE REDNECKS."