Hello there,

Hope you are doing well. See,it's very unlikely that that someone will  not be able to participate in the  Counselling process just because of changed address in Aadhar Card. As NEET and the Counselling process are conducted by two different authorities and NEET exam is over now ,the only job left is that of the Counselling authority.

Whenever you'll be registering for the Counselling process and during admission and document verification in the college you'll be allotted,you must provide your new address on the Aadhar card . However,when you'll report into the college you'll be allotted,you must carry both your aadhar cards with the old and new address in case it's needed . But while providing information during registration and admission into college,you should provide your new address.

Hope my answer helped.