Well, yes and no.
Vocal F0 range is mainly determined by the length and thickness of the vocal folds. Inasmuch as neck circumference correlates with the size of the vocal folds inside the neck, you could find a loose, indirect correlation between neck circumference and F0 range. For example, adults generally have thicker necks than children, and they generally have lower F0 ranges.
But there are several factors that contribute to neck circumference, and not all of them are associated with larger internal organs. For example, someone with a relatively high body fat index could have a very thick neck but relatively small vocal folds. Similarly, people who take up body building and build up all of the muscles in the neck will see an increase in neck circumference but not a concomitant decrease in vocal range.
If anything, neck length is going to be more reliable than neck circumference. The length of the neck is determined by skeletal structure, so it is more likely to be in proportion with the vocal folds. In the opera world, conventional wisdom says that the stereotypical tenor has a short neck and the stereotypical baritone has a long neck. But even that metric is not 100% reliable, since ultimately the growth of the vocal folds is independent from skeletal growth and can be influenced by such things as testosterone levels.