Another update, in case anybody else is wondering. I wished this information was posted up on their web site, but the only thing I saw were two FAQ's that kind of contradict themselves. After you submit your renewal, you will receive an email that says the following. This would had been helpful to know, as it pretty much answers my question...
Thank you for submitting your application for an Illinois Concealed Carry License. The Illinois State Police will issue your license pending verification all information is accurate and meets state requirements. Under normal circumstances, applications are processed within 120 days (or within 90 days if fingerprints provided). During the COVID-19 pandemic, and under the emergency administrative rules issued as a result of the state's disaster declaration, FOID card holders and CCL card holders who submit their renewal applications will remain valid during the duration of the state's disaster proclamation and for a period of 18 months following the termination of the disaster, even if their renewal application is/was not submitted prior to expiration.
If you have submitted for renewal and you are concerned about your current card expiring, see below:
Under the authority of 430 ILCS 66/70 ©, A license is invalid upon expiration of the license, unless the licensee has submitted an application to renew the license, and the applicant is otherwise eligible to possess a license under this Act. (Italicized for emphasis.)
The part that sticks out is the "FOID card holders and CCL card holders who submit their renewal applications will remain valid during the duration..."
So if anybody else is wondering, I feel pretty confident in saying that you submit your renewal before expiration, then take the class, then somehow submit your proof of the class to the state. I'm sure how we submit our proof will be my next question in about (hopefully) six months when all this is over.