While school grades cannot be used as the sole judging criteria to "measure" a person's intelligence; it does in fact reflect, roughly, a person's ability.
For example, while Stephen Hawking was indeed a slow starter, he aced his scholarships exams in Oxford, getting an almost perfect score in physics.
Schools do not always detect the genius in a person at a young age due to many standardised things, but this does not mean that test score do not reflect the brilliance or intelligence of a person.
While many famous scientists who have won the Nobel Prize have been slow starters, getting bad grades in school, most of them had excellent marks in college or university. It all just depends on when the person's intelligence shows, then it can be reflected in the marks.
Schooling is a bad way of measuring intelligence.
I did poorly in school, but I didn't have rights that I should of had in school. For example, every time I choose to choose an elective, I was told I couldn't do that course. I also was so afraid of people to like some teachers and students. Being offended by people in school can lead to bad grades. These are some reasons why based off my experience there are other factors that you can take into consideration.
There are many different types of intelligence that unfortunately most schools do not acknowledge. Yes, science and math is extremely important yet it does not account for the different types intelligence that could be collaboration, body intelligence, musical intelligence, and perhaps the ability of one to adapt to different circumstances. The purpose of school is to have people prepare for the future so if one has a musical talent instead of a math, science, or English skill, how can you appropriately account for that? Perhaps putting less weight on what they are not good at and more weight at what they are good at. This does not mean that one can teach someone to learn a skill or study much better. Rather, there are ways people learn differently from another. That musician I mentioned can learn math and science much faster and better if perhaps he or she learned it through music. The question you asked about a student's performance measuring a student's intelligence is actually counter intuitive because you can only measure, as it is now with tests, certain skills and aptitudes. Asking this question without measuring all types of intelligence can fail people and having a one size fits all view can cause assurance among people while perhaps making learning less efficient.
There are too many factors that go into determining intelligence. To determine it, and average must be made, but intelligence is not determined by school grades. A student with a tough teacher will do worse than one with and easy teacher, even if they have the same intelligence. Grades are also dependent on environment. An intellectually gifted person may fail a test simply because they couldn't study. Also, we are human. Some projects and exams count for insane amounts of our grades. Everyone messes up once and a while, but sometimes, it happens on the biggest, hardest assignment, and, as a result, grades plummet.
I know there have been many intelligent folks who have done poorly in their classes, and it irritates me when students think someone is dumb because of low grades. If you think about it, most of the education taught in schools basically tests your memorization. Just saying, it is true.