Probably not. By chemical testing if you mean biological monitoring for effects of workplace toxins, like lead, asbestos, etc., there's no point in doing this if a worker is not exposed to these substances by the nature of their work, even if the toxins exist somewhere else in the workplace. If you mean drug testing, this is a matter of company policy as it pertains to the drug free workplace act.
Should match risks. Testing in occupational settings should match the health hazards. For instance in an industry where there may be lead exposure there should be periodic blood tests to ensure there are no toxic lead levels. But if there isn't lead in the workplace you should have blood tests for lead. The bottom line is a safety or industrial hygiene professional should be identifying health hazards.