6 year old finally getting 'diagnosed' as autistic. Will private school reject him?

[GoodnessKnows]

I'm really worried about this. Obviously, if he's a pain in the arse (listens to his own rules but insistent on others following the teachers', etc. etc.), could they turn around and say that they can't cater for him? He's doing well there (please gd may it continue) under the care of an understanding teacher but I'm terrified to tell her of the CAHMS thing.
Also - on another topic, I'm worried about him as I'm awaiting the results of a tumour (thought, hoped and prayed to be benign) in my spinal canal. I've only known for a week and a half. It'll mean lots of changes. Feel for him and worry about what other children may say to him.

He was at a local and 'outstanding' state school before his current school but moved him. The teacher was outstandingly crap and intolerant of him. When he's diagnosed (bet my bottom dollar it'll be high functioning autism), I'd love to photocopy it, roll it up and shove it up her blummin' nose. Gosh, that's nasty. Sorry. Just feel soooooo angry with her. I do feel that tiny little ones (he was there from the age of 3.5 to 4.5 ought to be treated with a little more professional consideration - ie consider that there may be an underlying SEN vs shouting his name across the room and encouraging alienation (not one play date that year).
I'm also wary of sharing this diagnosis with .... anyone.
I know that some people get a private diagnosis for this very reason. If I get one through CAHMS (no mean feat), would I have to 'declare' it at school or holiday camps, etc.
has anyone had a camp, holiday club, an activity etc refused/ declined purely because of their DC's diagnosis.
Also (sorry to go on), what's with the 'asperges is now classed as autism' thing? His first cousin has asperges. He has it quite severely - 17 hours 1:1 given through it primary school once diagnosed. Question is: is it likely that my son's DS is asperges but just not labelled correctly?

Thank you. Clarifies hugely. He didn't have any speech delay and his communication skills are excellent - including eye contact) - IF talking about a topic that interests him. Otherwise, he can't wait to get away. Feels restrained.
He's bright - no educational SEN apart from
The need to have a magical teacher cajole him onto following instructions and doing the work set vs his own construction of it.