Not the parent, and I'm not saying it definitely wouldn't have happened (I have no idea), but it's at least possible. There was advance intelligence around the event that might have been treated differently by a different administration.
Even if it had happened, the response would also have been different.
In Richard Clarke’s book he details the intelligence community’s multiple warnings to the new Bush administration that spring and summer. They were ignored.
As Gore came from the Clinton admin he and the people around him would have had a lot more experience dealing with and familiar with the threats and actors, who were already known.
I have no idea; I'm just saying that with different people in charge, they wouldn't have reacted in exactly the same way.
If I had to guess, I'd say at least no Iraq war, if we consider that part of the response. Patriot Act probably would have looked different. I expect there still would have been military action in Afghanistan, but likely with differences as well.
Bush's team ignored Clinton's team attempt to handover what they knew about the threats (in these threads someone mentioned Richard Clarke's book, I remember reading a 2003 TIME article, you can probably also read the results of the congressional investigation).
If the Supreme Court hadn't done the shenanigans in Florida, Clinton's team would've been Gore's team, and who knows, maybe those hijackers would've been caught...
If you enjoy these kinds of hypotheticals, check out the series For All Mankind on apple tv.