Our DS is one of those you mention who got into a similar school from state primary with no specific tutoring, so you might not think our experience is relevant, but anyway...
We did a bit of tutoring in Year 5, but that was more to prep for state grammar entrance. We stopped the tutoring after a while because we frankly thought it was a waste of money - DS's practice scores were only improving a little, and this seemed to be largely because of familiarisation and speed, which he could easily practise at home - the few bits of content that were new (eg the odd maths concept) we could cover ourselves.
So, when it came to prepping for independent entrance, we decided not to bother with a tutor. The exam papers were significantly harder than the 11+, but there were past papers available so we worked through those at home, which did involve quite a bit of time on our part (teaching some new maths concepts, trying to model how to answer English comprehension questions etc) . He definitely needed that practice and input. Whether the school 'made allowances' in the exam I don't know, because I don't of course know how he did compared with others - but anyway, he got in. He's doing well and is in the top sets for maths/languages etc, so I have no concerns that he was given a place beyond his ability. It's possible that they were more forgiving of any errors/lack of polish in the entrance exams, particularly in the English paper, which was the most different from what he'd done at school - I suspect his maths/reasoning performance would have been pretty strong without any positive discrimination. With the interview, we trusted the school's advice and didn't do any prep at all.
So, based on our experience, it's not necessary to have specific external tutoring - but equally I wouldn't have wanted to send DS into the exams without a fair degree of preparation, so we did need to do that ourselves at home. In your case, though, it may be that your prep will do this for you?