Ok, after looking through the ISP site and reading the actual Act, I found this...
Link:
https://ccl4illinois.com/ccw/Public/AboutTheAct.aspx
430 ILCS 66/35
Sec. 35. Investigation of the applicant.
The Department shall conduct a background check of the applicant to ensure compliance with the requirements of this Act and all federal, State, and local laws. The background check shall include a search of the following:
(1) the National Instant Criminal Background Check
System of the Federal Bureau of Investigation;
Now, granted the license is only valid for five years and I highly doubt that it is issued to a prohibited person, it appears that the FCCL does meet this exemption... I, however am too poor and not brave enough to test the theory though...