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.
The Bush administration let the attacks happen.
https://en.wikipedia.org/wiki/September_11_attacks_advance-k...
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.
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.