I decided to look into the law more thoroughly. As it turns out, the guy is completely wrong and the law is not at all ambiguous.
Checking the public record: this guy was born 7/19/1994. His DUI arrest was 7/8/2015. In other words, he was under 21.
625 ILCS 5/11-501.8 deals with suspension of driver's licenses for persons under 21. It is a "statutory summary" suspension, meaning that an officer swearing he had probable cause to arrest for driving while impaired (any BAC over 0.00 with probable cause that ANY alcohol had been consumed) is required to submit to the Secretary of State, who is required to suspend the license.
So his license was unquestionably scheduled to be suspended 46 days after he received notice of the probable cause statement from the arresting officer.
This suspension is separate from the criminal charges. It is an administrative act and must be handled by the Secretary of State. Subsection (h) gives judicial review to the courts, but the courts are limited to, essentially, for the purposes of the administrative portion, to determining issues of notice and probable cause. They cannot, by their own power, undue a suspension as part of a plea. That power is granted to the Secretary of State.
The law then lays out the procedure for people who've had their license suspended under the Statutory Suspension to remove the suspension. Again, this must be handled by the office of the Secretary of State. A plea bargain is not a judicial review. The plea bargain only resolved the criminal suspension.
Under the statute and the subsequent rules promulgated by the office of the Secretary of State, he would have had to schedule an informal hearing, after the minimum waiting period, to be classified in a risk category. He would have to complete a DUI education class, and then pay a fee to get the suspension removed.
TL;DR: the plea bargain only stopped the criminal suspension. It had nothing to do with the administrative suspension. An administrative suspension is not reviewable by the court except for issues of notice and probable cause. Even then, only two courts in Illinois are given such authority, neither of which he was in.
The article is wrong.