Unless the schools are test optional 
The answer, as always, is “it depends”. I’ve written many times that in my opinion the key to academic success at tough boarding schools is excellent time management skills, not gradations of intelligence.
But, it really depends. How low is “very low”? How demanding is the current school?
I know a student at a boarding school with a median SSAT of around the 86th percentile, who had a 75th percentile score and who was on their first honor roll. But that’s not a kid with an SSAT in the 20th percentile.