I don't have specific experience (we had to rescind dd2's statement because we were moving abroad for a period -we were told that we would have to reapply when we returned) but there should still be any health services available, although there may be differences in method of provision (ie you might need to go to the clinic for slt instead of it being done in school, ditto physio, or etc) I'm assuming he has camhs support outside of school anyway, so that shouldn't be affected.
Obviously the1-1 support is not relevant, you have decided to provide that yourself in choosing to he. It might help if you could clarify which parts of the statement you are keen to continue - and the reasons for deciding to he. If the child has been removed from school because they are medically unable to cope (anxiety and stress can be corroborated by health professional/ camhs etc) then you may be entitled to some educational support for a few hours a week ( sometimes a tutor will visit the house, otherwise the lea might offer a place in an external unit)
Essentially they are not under any particular remit to provide any educational support unless you can prove that you were forced to he as your child can not attend school for x,y,z reason.
A lot depends on how friendly your lea are, though. And what ds's professionals think about your decision to he. If they all collaborate and agree that he can not attend school due to his mental health issues, then the lea should offer you some support, but it is likely to be only for a relatively minor percentage of the usual school attendance hours. There's very little chance they will offer ft tuition for 32 hours at home....
There are a fair amount of yahoo groups for home Ed /sn kids I think, might be worth asking them how they best deal with the system? I bet there will lots of advice.
My statemented kid is happily in school, but we are toying with he for ds1. (just ADHD, anxiety, some social difficulties). We will just be autonomous though as he doesn't qualify for any particular support.