I think it can definitely help a child pass, although I'm not sure it is always a good thing. I did have a discussion with one of the mums at school after her child passed. She told me her child had always been middle set for everything, but they called on the services of a tutor and they managed to pass the 11+ and secure a GS place . I do worry that a child in that situation might struggle to keep up, but she was confident they would be ok.
We had the opposite - my son was not properly prepared and narrowly failed one and passed another, fortunately he has still got a GS place. With hindsight I would do more home tutoring/ training to prepare them for the test, but we had some pretty extreme extenuating circumstances in the 2 years leading to the test and focussed rather late. And it didn't help the school were incorrectly grading my child. I don't think I would call on a tutor to push my child up through considerable grades, I'd be worried it might backfire in the future.