A hallmark of intelligence is the ability to find connections between the seemingly disparate.

That's also a hallmark of some mental/psychological illnesses (paranoid schizophrenia family) and use of certain drugs, particularly hallucinogens.

The hallmark of intelligence in this scenario is not just being able to make the connections, but being able to pick the right ones.

The word "seemingly" is doing a lot of work here.

Sometimes things that look very different actually are represented with similar vectors in latent space.

When that happens to us it "feels like" intuition; something you can't really put a finger on and might require work to put into a form that can be transferred to another human that has a different mental model

Actually, a hallmark could be to prune illusory connections, right? That would decrease complexity rather than amplifying it.

Yes, that also happens, for example when someone first said natural disasters are not triggered by offending gods. It is all about making explanations as simple as possible but no simpler.

Does this make conspiracy theorists highly intelligent?

No, but they emulate intelligence by making up connections between seemingly disparate things, where there are none.

They make connections but lack the critical thinking skills to weed out the bad/wrong ones.

Which is why, just occasionally, they're right, but mostly by accident.