this isn't a "it depends on what computation happens in this specific case" question, this is a "how does human cognition work".

Every website you visit has the payload delivered over the network before any JS is parsed. It has to, there's no other way. Same with intuition followed by rational thought

I'm not sure human cognition is that clear cut or linear.

I guess if you define all rapid cognition as Intuition and all slower conscious cognition as Rational Thought, you're right by definition, but while that might provide a happy feeling, it might not give you any useful insights upon deeper inspection.

For instance, it doesn't support or disprove the "less emotion is bad for thought" idea