The USCIS looks at any criminal offense for citizenship or deportation purposes. If the offense took place within three or five years of the 'filing' of the naturalization application, then this can create challenges. If the crime is based upon intent and knowledge, then the issue is whether the crime will be defined as a crime involving moral turpitude.
Whether the crime will be a basis for deportation hearings is unclear. The naturalization examiner will have carefully review the criminal law to determine whether a conviction based upon the Illinois criminal statute appears to be a crime involving moral turpitude. It is possible that your admission from a foreign vacation or simply filing for a green card renewal can result in an immigration court hearing.
I strongly recommend that you contact an experienced immigration attorney like our office.
The above is general information not meant to be legal advice. The above reply does not create an attorney-client relationship.