Yes, the district can qualify your on-the-job injury as a serious health condition covered by FMLA for those eligible. Designated FMLA leave can run concurrently with a workers' compensation leave, or with paid sick leave. While FMLA is unpaid leave, it does allow the employer-paid portion of your healthcare benefits, such as medical insurance, to continue during the approved period of up to twelve weeks.
Please also visit the Puget Sound Workers' Trust FAQ page for additional questions and answers regarding work injury claims.