The ASVAB can be studied for and grinded, though, like the SAT, it would require more effort with a low IQ. Iirc the breadth is less than the SAT. Is there another test you are referring to in terms of this "IQ test proxy"?

For fair disclosure, there was a study which showed that as IQ decreased, the span of time for a perfect IQ score prep increased almost infinitely, as the low IQ kids forgot the material they already learned. Maybe I will look for it later, would be very relevant here.