It does not seem so.
The link at the bottom of the article points to this article by Schmidt, Fox, Perez-Edgar and Hamer.
My (non-expert) reading of this is that baby fussiness is largely genetically determined, but that certain environmental factors also play significant roles.
We found evidence of a gene-endoenvironment interaction in predicting
two components of temperament in a sample of typically developing
Of course, this is not sufficient evidence to claim that intelligence and fussiness covary; merely that fussiness is to some degree inherited. Of course, intelligence is to a large measure inherited, too, but no link is drawn between the two.
An article at this link suggests that a probable test for early giftedness is whether babies easily habituate to new stimulus, which could mean that they can absorb and retain sensory information better. My reading is that the study is very cautious not to make any firm claims about infant intelligence being identifiable by common heuristics.
I found there are many supposed signs of superior intelligence on baby-advice sites (see for instance this link) most of which are some form of folk-wisdom. For instance, the claim that smarter babies do not sleep well has been problematised many times over. E.g. Here.