What you are planning to do is illegal. Depression is considered a disability under the Americans with Disabilities Act of 1990. If you have more than 15 employees, you are obliged to provide reasonable accomodations for such employees, and you may not discriminate against them while hiring.

It is also deeply unethical. If they've expressed some intent to not take it seriously, you'd have a point, but the idea that people with less-than-stellar mental health shouldn't have jobs is completely sickening.