They can be, yes. Under the Americans with Disabilities Act (ADA), an individual with a disability is a person who:
The ADA prohibits private employers, state and local governments, employment agencies and labor unions from discriminating against qualified individuals with disabilities in job application procedures, hiring, firing, advancement, compensation, job training, and other terms, conditions, and privileges of employment.
If an employee informs you that they have anxiety or depression and requests an accommodation, you should begin the interactive process. Basically, you and the employee determine what, if anything, can be done to accommodate them so that the essential functions of the job get done to your standards and the employee is able to continue to have the equal benefits and privileges of employment. As part of this conversation, you may request a doctor’s note to substantiate the disability.