Do we even know if Delia is Ash's real birth mom? Maybe Ash was adopted.
Well, IF Ash was adopted, that would certainly explain Delia's surprised exclaim about whether Ash had a twin brother or not (since, honestly, had she given birth to Ash, she certainly would have known if he did have one or not).
As for the topic, probably not. For one thing, Giovanni and Ash met only once in the entire series (that being Mewtwo Returns), and they treated each other as if they were complete strangers. Given the close proximity between Pallet and Viridian, had he been Ash's father, Giovanni, at the very least, would have some idea. Plus, the only suggestible reason why Giovanni even wants Ash's Pikachu (and we don't even know if he himself actually wants it or if JJM seemed to just presume he wanted it) would have been its abnormally large power.
@KirbyChu: I know he was a storyboard director, but I'm pretty sure the interview in question also mentioned that he was the director of Pokemon at one point (I think the introduction, if I'm not mistaken, and I think it was from season 1 all the way up to Season 9, or for non-seasons, from the beginning of the Original series all the way up to the end of DP), so I'm pretty sure that, up until DP, at least, he had some control over the story.