Yes, it's highly unlikely a child at a state primary school will have covered most of the types of questions in 11+ tests.
The English comprehension and writing are far beyond year 6 level and although it's possible some children will have the extensive vocabulary required (if they read books aimed at higher ages widely and look up words, or if they have a highly literate family who use an unusually wide vocabulary talking to children), for the majority it would take a huge amount of extra learning.
My own dc is at "greater depths" in all subjects at primary school, but would have needed at least a year's tuition in English and extensive practice to pass the test. DC loves maths so might be ok in that without tuition, but would still need to be taught exam timing and skills and the extra 11+ topics that aren't taught at primary school.
We've done some non-verbal reasoning and DC loves it, finds it fun and easy, but of course needed me to teach and explain it before getting the hang of it.
There's also the exam technique. For example, as DC has been practising bits of verbal reasoning with me and can do ten minute tests and get 100%, we thought a school test would be ok. But dc can't finish the longer tests in time, despite the questions being the same type, style, etc..
We decided not to try for private schools because of the enormous amounts of work and pressure it would involve, and that's with a child who consistently achieves highly at a state primary.