No. Your Employer should only receive works status reports from your doctor, stating whether or not you can return to work. In a way, the worker’s compensation insurance carrier operates similarly to your car insurance if you get into an accident.
You call your insurance, report the accident, and they take it from there. You don’t have any further contact with the driver of the other vehicle. The worker’s compensation insurance system is similar, your employer sends their Form 5020 “Employer’s Report of Injury” to their insurance. After that, you are dealing with the insurance company rather than your employer. The insurance company communicates with your employer on whether or not they can bring you back to work.
By law, your employer is only permitted to receive “work status reports” from your doctor stating your work restrictions. Your employer does not get any input in who your doctor is, or what treatment you receive.