There are two factors that come into play when answering your question.
1. If the rental agency actually does a car rental drivers license check
Generally, car rental companies will state that "your rental may be subject to a drivers license check.." Not every single renter and additional driver is necessarily checked, but it's not something that you would necessarily know in advance. If both you and your employer are there (they to rent the car and you to sign on as an additional driver) only they may be subject to a car rental drivers license check, or you may both ... or neither of you may be.
The only way to be sure would be to contact the particular car rental location prior to pickup to find out their particular dmv check policy for additional drivers.
2. The other factor has to do with what is looked at, IF you were subject to a drivers license check
It's common for a car rental company to refuse a renter/additional driver for some standard criteria:
See Car Rental Drivers License Requirements
... but these criteria can vary a bit from company to company.
If your court dates are after the pickup date of the rental car and you have less than 3 accidents, I would think you would be fine... but again, it would be best for your employer to contact the specific car rental facility for details on their particular requirements with regards to car rental drivers license check -- for an employee or for additional driver.
One other thing that you may want to check for is if your company or your employer has a contracted corporate account with a particular car rental company.
Generally, when a company has a corporate account and someone picks up a rental car for a business rental, fellow employees are permitted to drive the vehicle for business purposes (as long as they meet the minimum age requirement and have a valid drivers license), but need not be present at the time of pickup to show a drivers license or credit card, therefore no drivers license check would be performed.
If it is a business rental and there is a corporate account, your employer should check into the particulars of that account with regards to additional drivers.
Pages from this site, relating to this topic:
Car Rental Policies Index
Business Program Benefits