Hi Brent, You ask about how to have the interactive discussion regarding accommodation. In the case of your candidate, she has already volunteered that she struggles with depression, so the next logical step is to have an interactive discussion about possible accommodations. That discussion should be well-documented, perhaps by a written letter afterwards that summarizes what was discussed, what can be offered, and what cannot be offered.
Your question seems to go more to the question of whether we should ask people as a matter of course whether they have any issues that need accommodating. I would suggest that you not go fishing for disabilities even by questioning about accommodations. There are two problems. The first is the same problem that arises if the testing is done inappropriate—it raises the question whether you are screening people out because of disabilities. The second problem is that you are volunteering to go to more work and trouble than is necessary. Just because a person has disabilities does not mean that he or she needs accommodations. It may be safer all around to wait until the person volunteers this information (unless it gets picked up by post-offer screening).
You also mention other potential discussions about needs in the family. These might relate to disabilities or might not. I think it is fine to ask candidates something like, “Are there any issues with your family or children that you would like to make us aware of, that might affect your placement or how we support you, such as special circumstances with your family at home or special care needed by anyone?
A very broad question like this could deal with any type of issue, not just disability, and lets the candidate choose whether or not to share. Perhaps it was in response to this type of question that your hypothetical candidate shared that she has depression! If the question is documented, the response will be documented as well. It can then go nowhere, to an interactive discussion about accommodations, or to other discussions such as how to educate children or care for ailing parents.
Disclaimer: not official legal or psychological advice or opinion