Personal Independent payment, does carer's allowance get backpaid?

Hi

I have applied for personal independent payment and is on hearing i am not going to hearing and have been told by hmcts that it could take minimum 6month is this true or has anyone got any earlier date than 6month and i got reminder email sent from hmcts to send any evidence is this auto email or its not auto email also i like to know i i win pip award for example after 6 month i know that they will payback date pip award what about carer allowance because carer allowance dont pay untill is applied and we cant apply for carer allowance until we get pip award ? Cheers