That's not the case at all. The Trojan Horse is his gameplay Noble Phantasm, and that's as far as it goes. The only time I can remember it being referenced in any story is Avicebron's interlude. Out of Odysseus' two Noble Phantasms, Troia Hipos is by VERY FAR the lesser of two evils.
What his actual characterization focuses on is his harem LN protagonist-like status, Calypso, Circe, and Nausicaa all falling for him despite his absolute unwavering loyalty to Penelope. He's portrayed as a completely nice man with no filter for complimenting others, causing ladies to assume he's interested in them. That's a terrible take on Oddy for multiple reasons, but one-noteness isn't one of them.