Yes, if there is an underlying trace nutrient deficiency there is likely to be several underlying trace nutrient deficiencies and vitamins and minerals work together as complicated teams so intelligence might be helped by the use of a supplement that provides the recommended daily allowance of trace nutrients.
In the last post I highlighted the iodine and selenium content of the supplements that were given to 8th and 10th grade students, , because iodine is the trace nutrient that has been associated with IQ in a large number of previous research studies and selenium is important in the enzyme that breaks down elevated levels of thyroid hormone. Not all students were helped. But the general intelligence was improved for forty five percent of students who were from both more well-to-do and less well-to-do communities. this suggests that trace nutrient deficiencies may be a more widespread problem than is recognized.
The B vitamins and other nutrients may also have helped in addition to the iodine and selenium. But testing all the nutrients as individual supplements might have not helped the 45% of students as much or at all because trace nutrients work together in complex metabolic pathways.
What is encouraging about the research study is that the fluid intelligence of older children was helped by the simple solution of a once a day vitamin and mineral supplement. This suggests that throughout the lifespan daily decision making skills could be aided by preventing trace nutrient deficiencies. We think and learn throughout the lifespan not just during our school years. 
But, no, a one-a-day nutrient supplement might not help some people if they have a metabolic difference that makes them unable to use the form of the trace nutrient commonly used in basic one-a-day supplements. And a high dose form might even hurt them.
Some individuals may have a defect in their ability to change an inactive form of folic acid into the metabolically active form that is found in foods. Individuals with a methylation problem who take a high dose supplement of folic acid may become more at risk for trace nutrient deficiencies because the supply of folate that they are getting from foods may become more difficult for the body to access because of the oversupply of folic acid. Identifying which individuals need the methylated folate form instead of the more commonly available unmethylated form of folic acid would be important to reduce the risk of a one-a-day supplement potentially being harmful instead of helpful. [3, 4] Some people may do better taking a trace mineral supplement and eating split pea soup and other foods that are naturally good sources of folate rather than taking a mixed vitamin supplement.
We need iodine throughout life for health as well as intelligence. Iodine deficiency may be involved in breast, prostate and lung cancer.