I don't know if its natural, many people can get depressed, but SEIs problems with the hard demands of life can lead to depression. For some SEIs the solution can be to find a rich partner, or to find a job that is not too demanding but not too boring either. Also use free time for some personal "SEI stuff", and that way compensate for a boring job. Or to bring in more fun and partying into life. It's also important to have Alpha NT friends, I feel that they give me much.
But I wouldn't say that SEI is a particularly depressive type, but some problems are usually present. They are also quite good at coping with negative stuff, because of the rich inner life (Si).