Anything which is correlated to IQ, certainly including academic achievement, provides some information about IQ. So if someone is doing better/worse in school than his score on an IQ test predicts, you should revise your estimate of his IQ up/down, although I can't say by how much.
In a magical world in which every child gets equal and adequate:
- sleep
- exercise
- healthy food
- parental support (in all domains)
- social interaction
- individual instruction
- environmental stimulation
- play
- etc.
Then yes, your hypothesis would be correct... any variation in school performance would require a revisiting of their IQ. Except there are biological influences to consider, so the kids would also have to be clones.
Here in the real world, however, we often have to look at other factors, because life is complicated.
