Thanks for writing. While I’m not a lawyer I believe if your physical practice is ADA exempt your web presence, as an extension of that physical business would maintain the same exemption status. If you’d like to be absolutely certain I’d confer with an ADA lawyer (email us, questions at yokoco dot com if you need a referral) but I don’t believe you have reason to worry.
The ADA states that a "covered entity" shall not discriminate against "a qualified individual with a disability". This applies to job application procedures, hiring, advancement and discharge of employees, job training, and other terms, conditions, and privileges of employment. "Covered entities" include employers with 15 or more employees, as well as employment agencies, labor organizations, and joint labor-management committees. There are strict limitations on when a covered entity can ask job applicants or employees disability-related questions or require them to undergo medical examination, and all medical information must be kept confidential.
UPDATE: Since writing this post in August 2017, several important changes have taken place in the laws regarding ADA compliance for websites. On December 26, 2017, the Department of Justice announced that they have withdrawn the Obama-era Advance Notice of Proposed Rulemaking mentioned in this article which intended to require ADA website compliance. The DOJ’s withdrawal announcement stated, “The Department will continue to assess whether specific technical standards are necessary and appropriate to assist covered entities with complying with the ADA.”
If you have a disability and are qualified to do a job, the ADA protects you from job discrimination on the basis of your disability. Under the ADA, you have a disability if you have a physical or mental impairment that substantially limits a major life activity. The ADA also protects you if you have a history of such a disability, or if an employer believes that you have such a disability, even if you don't.
Under Title III, no individual may be discriminated against on the basis of disability with regards to the full and equal enjoyment of the goods, services, facilities, or accommodations of any place of public accommodation by any person who owns, leases, or operates a place of public accommodation. Public accommodations include most places of lodging (such as inns and hotels), recreation, transportation, education, and dining, along with stores, care providers, and places of public displays.
Talk to your web designer about other techniques that will make your site more user-friendly for people with disabilities. Worried that’s not in your budget? Consider the fact that DOJ fines start at $75,000. And it's still yet to be determined if a non-compliant website is liable for one fine or will be charge per page for each violation. As the recent lawsuits illustrate, though, settlements quickly add up into the millions.