It has been noted that a noticeable percentage of ALL surgery patients suffer some post-op depression, even though the surgery was successful. This has been found also in living kidney donors, although it is hard to get an exact figure regarding depression. And of course if the transplant is unsuccessful there may be even more risk of post-donation depression. So the hospital does have to take into consideration whether the potential donor has suffered from depression in the past. As Clark well noted, each hospital has its own policies, and each potential donor is evaluated individually. And if a person who had suffered from depression in the past is approved to donate, it would of course be important to warn him/her of the risk, and to be alert for signs of depression if they do occur after the surgery. Organ donation is such a wonderful life-affirming act that we can be tempted to think that ALL donors will feel on-top-of-the-world after donation, but this is not always the case.
best wishes,
Fr. Pat