If you fulfill the eligibility criteria required for AIIMS MBBS, you can apply for the exam. Domicile is not required and it will not impact much on the admission process. 

In the AIIMS MBBS application form, in the field asking for 'State of Domicile' you can fill the state where you are residing.

You can fill the aiim form without the cast certificate but you need to fill I under general category.

If you want to filll under obc category, then you need cast certificate.

If you are saying where status is OBC caste and also you are domicile status then you need to include the supporting documents to prove your claims therefore it is mandatory to have a caste certificate in domicile certificate it may be required at some point of time to prove The authenticity of the data provided by you and to give the admission to the genuine candidate therefore try to make them as soon as possible to avoid any kind of inconvenience.