In the case of injury or trauma, police officers are subjected to more tests than the average person to ensure that they are physically fit to return to duty. If, say, Coleman were injured on the job and had to be treated, tests may indicate that something was awry (elevated liver enzymes, etc.). Further tests would be ordered, and the Docs would most certainly know--not that his 300+ pound off-season body wouldn't be a clear enough indication.
Theses findings would not be reported to the employer however, just the insurance company. If they want to drop him because of his 'addiction' it is at their discression. But, the Police Department itself would not be involved unless someone wanted to make a stink 9i.e. someone with a personal beef against another officer).