To me it will depend on whether the child’s school gives them enough practice in the type of test they’re going to encounter.
We lived overseas until dd1 was 10. She had precisely one term after we returned to the U.K. before the 11 plus. At the time it was all verbal reasoning tests, and although the English-speaking school she’d attended was very good, she’d never even seen such tests until the beginning of that term.
The school (an independent - we couldn’t get her in anywhere else at relatively short notice) gave them daily practice, and at the beginning she was scoring maybe 40-45%. Of course we were concerned, but a friend of MiL* - who ran a private prep school! - said the tests were designed to ‘detect potential’ so practice wasn’t necessary.
Which was obviously rubbish, since by the end of that term, dd’s scores were averaging about 90%. She passed the 11 plus, ended up at a RG university and later added an MA to the BA.
So yes, I do certainly think tutoring can help, and it doesn’t mean the child is necessarily going to struggle at a grammar.
*Of course we and MiL were livid with her for suggesting that dd lacked potential!