I recently drove through IL on my way to Denver. To be legal the gun must be in a case and unloaded, ammo can be stored in the same case. I just put my Sig in a nanovault with a loaded mag next to it, locked it and left the key in and put it in front of my seat. It only takes a few seconds to have the gun out and loaded, probably quicker that trying to draw from IWB holster seated.
To also give you further peace- the link below is from the Illinois state Police.
If you look at #3 (Are out-of-state concealed carry permit holders granted reciprocity in Illinois?) in the FAQ it answers your question
Illinois State Police | Concealed Carry FAQ