So, it could be that if the stock of the weapon IS the carrying case. And the magazine is in the stock of the weapon, separate from the action/receiver/magwell the weapon could still be considered loaded under IL law?
The issue I see is whether or not the stock would be considered a case or part of the firearm. If it is considered the latter rather than the former, then you have just inserted a loaded magazine into a firearm, it may not matter that the firearm still can't operate. Basically, I think you'd be treading in a gray area that has too much potential to get one cuffed and stuffed for me to be comfortable trying it.
If this all seems rather silly, that's because it is. One thing I definitely don't miss about IL are some of the more Draconian gun laws.