A funeral home is a situation where there will be plenty of people who need a helping hand, and who better to understand and offer it with compassion than someone who deals with depression everyday. I worked in the chapel at the base, when I just starting to get better. Lots of people in pain came through that door. The two younger people, who were supposed to know how to handle "situations" had no concept what to do or how to speak to them. I did know.
That said, I would go to the interview and do the best I could. If I did get hired, I'd concentrate on learning what needs to be learned and doing my best. I would probably also make a decision about a test period of time--say 3 weeks--just in case it did make me more depressed, even after I'd given myself a chance to adapt.
If it was taking me down more than helping others was lifting me up, I would leave then. Probably lots of people interview with a similar plan. I'll bet that the people who haven't had problems quit more and faster than the ones who have and understand people's pain.