Could this happen in Chicago?
I am not sure. For any contract (marriage, real estate…etc) to be valid both parties need to know what they are agreeing to. If there is an essential part of the contract that one party keeps from the other then the contract is voidable.
So, if you lie about something essential to the marriage that had your spouse known about they would not have married you, you could face an annulment (the voiding of a marriage). The question is: Does “essential to the marriage” take into consideration cultural factors (such as religion) or does it use the “average person” standard?
The Illinois Statute does not clarify what kind of standard should be used when determining fraud in a marriage. I doubt that there is established case law on the matter. Thus, this is just one of the many gray areas of family law where “I don’t know, it depends on how the judge interprets the law” is the best answer.
For more information on the meaning of marriage please see What is a Marriage?