If I get hurt playing recreational soccer after work, will my employer insurance cover my medical/hospital expenses?
I believe you're confusing "Worker's Compensation Insurance Coverage" for "Supplemental Medical/Health Insurance"
Per your comment: Worker's Compensation coverage is coverage that your employer is (usually) required to obtain. This covers you during work-related injuries and is of no cost to you.
Medical / Health Insurance coverage is coverage that you purchase for yourself (and optionally, your dependents). This can be purchased independently, or can be purchased through your employer. However it's purchased, it is your coverage to use. You should take some time to familiarize yourself with the plan that you purchased, and its coverage, and your liability under the plan.
EDIT: Assumptions were for U.S. (sorry for not inquiring about your location). Answer has been updated to reflect a less US-specific response. Canada does have laws regarding Worker's Compensation, though. Might want someone with Canadian expertise to chime in.
EDIT 2: Per @ChrisInEdmonton's comment, I've updated terminology to reflect Canadian products