Yes. The short term disability or long term disability claim will run concurrently with the workmen's compensation claim, and any income payments received from WC would be an offset to the STD or LTD benefit payments.
Please note that the long term disability insurance FAQs are for state employees only. The state of Tennessee does not offer long term disability insurance to higher education employees. If you are a higher education employee, direct questions on LTD to your agency benefits coordinator.