It seems that if the FFL is located in a homerule town then they are exempt from Cook County mag limits and they can transfer anything that is legal statewide in Illinois.
What is a homerule town?
But yes, it depends on the FFL. My current one in Cicero does not care if I have a Chicago address as I ordered a Caracal 9mm which you know how big the mags are.
Of course to be legal, the gun is not kept in the City of Chicago because it is not able to be registered.
Now, the legality of transporting a new firearm with a higher than 12 capacity through Cook County from the gun store to its destination before it has been registered anywhere is something I do not know.
I think there is a grace period of 5 days or something in Chicago. So if I got pulled over on my way back from Cicero with a new firearm that is legal in Chicago but I have obviously not registered it yet, but do intend to within the 5 day grace period, I might not get put in jail!
I would like to add some experience showing the police my CFP (Chicago Firearms Permit) but I have not gotten pulled over for anything. I keep my license, FOID card and CFP card with me whenever legally transporting firearms to the range or gun store etc.
Can't wait for concealed carry.