you don't need to tell them you have SP. especially if you haven't been diagnosed with it yet. from what i gather, they would be more worried about physiological conditions, or extreme mental conditions like schitzophrenia. Many people without "mental disorders" still see councellors/psychologists so it's not like they would know you have SP if they are receiving invoices for councelling.
You can ring any health insurance company and ask what their policy is. you don;t have to tell them your mane - just make an anonymous inquiry.
The insurance my family has none of us had to tell them if we had any conditions or anything. You just paya set rate for whatever benefits you want to receive. If you want to be reimbursed for seeing a psychologist it may be more expensive, but seeing you're only 20 i'm sure there are government rebates for that.
Don't be afraid of talking to your doctor. everything you say is confidential, and he won't have any connection to health insurance companies so it's not like you need to be worried about him telling them or something.
Insurance companies will take anyone as a customer. They rely on revenue from sick people. But it's not like SP is a major liability, like a heart condition or something. All they would have to pay for are councelling sessions, it's not like u'll be hospitalised, so try not to worry about it so much.
I know heaps of people in their twenties who don't have health insurance, and i wouldn't bother getting it myself until i'm older.
Just go and see you doctor, they'll be able to advise you on what to do.
hope this helps!