Hi,
I'm also autistic and have multiple mental health problems
I applied to top unis (not Oxford and Cambridge) and got accepted into all of them; I would say that for me, it helped them understand my personal statement a bit more, and they have experience with autistic students so know what they are capable of
It also means that they will initiate the support setting up for you however, if you don't feel comfortable, I totally understand that, and once you've picked your uni, you can email the support team and set up the support
The one thing is though if you are applying where you need to do an interview or exam etc then it is definitely useful to let them know as you get adjustments and like they will understand why you might take longer to answer questions etc.