Good question! The sort of intersex condition you’re talking about is called ‘true hermaphroditism’ because the individual will have testicular AND ovarian tissue.
I don’t think they would be able to self-fertilise, because either their testicular tissue or their ovarian tissue wouldn’t function normally… i.e. they either wouldn’t produce sperm or they wouldn’t produce eggs and menstruate. There aren’t any cases of true hermaphrodites with both functioning ovaries and testes as far as I know.
In fact, in most cases neither tissues would function properly and they would be completely infertile. There have been cases (less than 15 I’d say) when true hermaphrodites HAVE got pregnant, but the sperm has come from another person.
It think if they could they probably shouldn’t since the babys DNA from sperm and egg would come from the same place-there are lot of health risks for incestuous babies (where the parents are related) and this case would be far more severe!!