The green glow and extra damage to undead did get mentioned as side-effects of reforging the sword with starmetal by the master bladesmith, back in Azure City.
But can we be sure that the Greenhilt sword wasn't already in the process of becoming a Weapon of Legacy even then? If so, then the glow might have been incorporated into the Legacy effect as the sword 'evolved' with Roy's adventures and his continuing dedication to it.

And possibly it did none of this for Horace because to him, it was just 'my sword'. He took good care of it and used it well, but he didn't have a problem with handing it off to Roy in the middle of battle. To him, it would have been the tool of his trade, but not a symbol.