There is probably no numerical data connecting constant thinkers and IQ, because the term “constant thinker” is not easily quantified. IQ is certainly closely connected to what someone thinks about, rather than how much they think. Socrates is reputed to have said “Strong minds discuss ideas, average minds discuss events, weak minds discuss people.”
However, if by “constant thinkers” you mean people who are almost totally absorbed in thought most of the time, then my opinion, based on anecdotal evidence and historical accounts, would be an unqualified “yes.” It is certainly true that those who have made the greatest intellectual achievements were constant thinkers in that sense. Furthermore, these constant thinkers were also of high IQ. For example, when Archimedes of Syracuse (c. 287 BCE – 212 BCE), recognized as the greatest mathematician in the ancient world, was asked the secret of his many remarkable discoveries (including integral calculus and the principle of hydrostatics) he explained that he was constantly thinking about things.
Such preoccupation often manifests as the kind of absent-mindedness that Isaac Newton displayed when he was mulling over a problem. On one occasion Newton, having abandoned his dinner guests, was found in a hall pondering a problem. During his absence, a mischievous guest gobbled down Newton’s dinner. On returning, Isaac peered at his empty plate, strewn with chicken bones, and replied, “Oh dear, I thought I had not yet dined.”
Mathematicians and scientists, including Henri Poincaré, Francis Galton, and Donald Coxeter are famous for stories describing the all-pervasive nature of their thinking. Even when participating in leisure, ideas percolating in their subconscious would emerge as Eureka! flashes of insight. Francis Galton, one of the pioneers in the study of heredity, describing his discovery of the concept of correlation, said:
The circumstances under which I first clearly grasped the important generalization that the laws of Heredity were solely concerned with deviations expressed in statistical units, are vividly recalled to my memory. It was in the grounds of Naworth Castle, where an invitation had been given to ramble freely. A temporary shower drove me to seek refuge in a reddish recess in the rock by the side of the pathway. There the idea flashed across me, and I forgot everything else for a moment in my great delight.
More recently, Computer scientist Gregory Chaitin, cofounder of what is called Kolmogorov complexity described how his unconscious made connections:
I’m a great believer in the subconscious, in sleeping on it, in going to bed at 3 a.m. or 5 a.m. after working all night, and then getting up the next morning full of new ideas, ideas that come to you in waves while you’re taking a bath, or having coffee. Or swimming laps. So, mornings are very important to me, and I prefer to spend them at home. … I think of the subconscious as a new chemical soup that’s making new connections, and interesting combinations of ideas stick together, and percolate up to full consciousness.
Similar testimonials have come from Jonas Salk (discoverer of the polio vaccine) and Ray Kurzweil, who was referred to as “the ultimate thinking machine,” by Forbes magazine. It’s safe to say that those who are constantly thinking about problems and immersed in their solution are generally at the high end of the IQ spectrum.