No, asking all employees about the prescription medications they are taking would be considered a disability-related inquiry under the Americans with Disabilities Act (ADA). A request for such information is generally not job-related and consistent with business necessity, according to the Equal Employment Opportunity Commission.
In limited circumstances, however, certain employers may be able to demonstrate that it is job-related and consistent with business necessity to require employees in positions affecting public safety to report when they are taking medication that may affect their ability to perform essential functions. Under these limited circumstances, an employer must be able to demonstrate that an employee's inability or impaired ability to perform essential functions will result in a direct threat.
For example, a police department could require armed officers to report when they are taking medications that may affect their ability to use a firearm or to perform other essential functions of their job. A fire department, however, could not require fire department employees who perform only administrative duties to report their use of medications because it is unlikely that it could show that these employees would pose a direct threat as a result of their inability or impaired ability to perform their essential job functions.
Source: EEOC Enforcement Guidance on Disability-Related Inquiries and Medical Examinations of Employees under the Americans with Disabilities Act (ADA), http://www.eeoc.gov/policy/docs/guidance-inquiries.html.