I wouldn't chance it. I make it a point to avoid Chicago (and as a result Illinois till they get a CCW law in place and even then I'd avoid Chicago like the plague) if I'm going somewhere.
That often results in me making a long trip around Lake Michigan via the UP and down through the LP, cut across on the ferry from Manitowoc to Ludington or make the long loop down south of Illinois by way Iowa and Missouri. Sure that adds a lot of time, distance and expense to my trip but it keeps me out of an area that I may end up paying a much more expensive price were I to travel through and be stopped.
Since you have no choice but to go there your choice is your choice and you have to live with the consequences if anything should happen depending on what you choose to do.
This is who we are, what we do.