and if she did so:
Does the Iliad mention this alleged daughter?
Was Menelaus the father or was it Paris?
Helen is not a historical figure, nor is the Iliad a historical text, and this question is better suited to, say, /r/Classics. But since there is no shortage of classicists around here:
Hermione is not mentioned in the Iliad, but she features in the Odyssey. At Odyssey 4.12 Hermione is said to be the daughter of Menelaus and Helen, and half-sister of Megapenthes, whose mother was a slave woman. Homer specifically says that Helen only had one child, Hermione, but Hesiod knew of a tradition in which Helen and Menelaus had a son as well, Nicostratus. The two sons became conflated with each other often in later tradition and at Rhodes were comparable to Castor and Pollux. In Homer, Hermione is promised to Neoptolemus at Troy, but the later tragedians wrote a tradition in which Menelaus promised her to Orestes, resulting in conflict between them--this is the tradition that Ovid favored, although of course he knew both.