Of course some do! Some don't though!!!
This isn't a private school versus state school thing. All independent schools are utterly different.
FWIW, my little one goes to an independent school that is truly excellent with dyslexia and other SEN.
All schools are different, but the main advantage you get in the independent system is CHOICE.
Go, look around, ask a hundred questions, find out general outcomes, have tester days, ask more questions....
In my DD's school they have a track record of successfully using scribes and laptops for several students in GCSEs when they get older. Knowing that was reassuring. Is your school all through? Or just up to 11, 13? Ask where they send children to after that and really dig about advice and help for the future.
My DD also went to a different pre prep in another area entirely years ago, and started there at age 3, completely non verbal. They were great too.