Legal Question in Education Law in Illinois

Yes. Home schooling is very liberally granted in Illinois. As long as you are doing a decent job and have notified the school, you should be okay, unless the child is the subject of a court order requiring someone else's consent. For example, if you are a joint custodian, you will normally need to get approval of the other custodian, as otherwise you risk a custody modification suit by an irate other custodian claiming they want the child because it needs to be in school. The other custodial parent might well win that suit if the Judge thinks the kid should be in public school.