A parents verbal consent to allow their underage minor child to have casual sex with an adult may in-it-self be a violation of state law. It will not protect an adult from prosectution.

A parent may consent to a marriage for a minor child 16 or or 17 years old by signing consent forms in front of a court clerk or a judge.

You are correct, it appears we inserted the law on predatory sexual assault. This law is used in some statutory rape situations; however, in the situation described in this question, the statute 11-9.1. Sexual exploitation of a child - is more likely the law that would be applied by a DA. This punishment could be in the "Misdemeanor" or "Felony" class.

(Updated below)

The term "Child" used througout the statutes is defined as anyone under the age of 17.

Sec. 11‑9.1. Sexual exploitation of a child.

(a) Any person commits sexual exploitation of a child if in the presence of a child and with intent or knowledge that a child would view his or her acts, that person:
(1) engages in a sexual act; or
(2) exposes his or her sex organs, anus or breast
for the purpose of sexual arousal or gratification of such person or the child.

(a‑5) A person commits sexual exploitation of a child who knowingly entices, coerces, or persuades a child to remove the child's clothing for the purpose of sexual arousal or gratification of the person or the child, or both.
(b) Definitions. As used in this Section:
"Sexual act" means masturbation, sexual conduct or sexual penetration as defined in Section 12‑12 of this Code.
"Sex offense" means any violation of Article 11 of this Code or a violation of Section 12‑13, 12‑14, 12‑14.1, 12‑15, 12‑16, or 12‑16.2 of this Code.
"Child" means a person under 17 years of age.
(c) Sentence.
(1) Sexual exploitation of a child is a Class A
misdemeanor. A second or subsequent violation of this Section or a substantially similar law of another state is a Class 4 felony.

(2) Sexual exploitation of a child is a Class 4
felony if the person has been previously convicted of a sex offense.

(3) Sexual exploitation of a child is a Class 4
felony if the victim was under 13 years of age at the time of the commission of the offense.

(Source: P.A. 94‑140, eff. 7‑7‑05.)

Marriage laws for minors in Illinois

If 16 or 17 years old, you must bring a copy of your birth certificate and another form of identification that shows your date of birth. Each parent or legal guardian will be required to sign a sworn statement consenting to the marriage or a judge must sign the consent form through an emancipation process. All forms must be signed in front of the court clerk at the time the application is filed. All parties must show proof of their identity with a driver's license or state ID card, a legal passport document or an Illinois Department of Public Aid card. If a parent is deceased, a death certificate or proof of guardianship or a court order waiving consent must accompany the application. For legal guardians, certified guardianship papers are required.

If you are under sixteen (16) years of age, you cannot get married in Illinois.