We are not aware of anything that would prevent you from obtaining proof of concealed carry licenses from your employees (note that a concealed carry license requires a FOID card), and that very well may be a best practice. Employees that carry firearms without being licensed could be subject to criminal penalties (see the Illinois State Police’s FAQs).
Also note that the Firearm Concealed Carry Act requires the Department of State Police to maintain an online, searchable database of all licensees. 430 ILCS 66/10(i). This database is not yet available, but it should provide another viable means of verifying an employees concealed carry license.