"She adds that she has no sisters."
Translation:Ella añade que no tiene hermanas.
This is hard to explain because double negatives in Spanish don't translate to double negatives in English. That's like saying 'She doesn't have even a single sister.' or 'she doesn't have any sisters, not even one.' It communicates her lack of sisters, but it's not exactly the same.
You don't negate nouns in Spanish, you negate verbs. There is a significant difference, yes. You can also add negative adjectives with more information (not even one), but you must negate the verb. That's what makes the sentence negative. It's not a stylistic preference, it definitely matters. Otherwise, it's as if you said 'she does have children not.' or some other strange nonsensical structure.
John_Doe is right. This isn't that object (ese/esa). This is just the difference between 'she adds she doesn't have sisters' (very strange construction) and 'she adds that she didn't doesn't have sisters. You can't just look in a dictionary and substitute word for word. 'Esa' is to point at a noun (that one) not to substitute in every instance where English uses 'that'. I'm sure you've noticed that the word 'it' can be tricky for English speakers too.