Alopecia in its own right is not classed as a disability in legal or employment terms. For something to qualify as a disability, it needs to have a substantial and adverse effect on your ability to carry out normal day-to-day activities. Alopecia itself does not limit the ability to carry out normal day-to-day activities but the mental health impact can.
Any consequential mental health issues, such as anxiety or depression may fall into the disability definition but alopecia alone does not.