Nope! You can use the CBSE admit card as your DOB certificate but not as Domiciliary certificate. For Domiciliary certificate you can visit your District Magistrate office or SDO office with documents and you can ask the officials about the procedure for issuing domicile certificate. It is not a hectic process. Based on the state policy, you will be asked to submit some documents and on the basis of that the DM will issue your Domiciliary certificate. You should do this and you will get it before the counselling for NEET starts. So don't worry about it.

To know more about NEET Domicile criteria  visit the link below:

https://medicine.careers360.com/articles/neet-domicile-criteria

I hope this answer helps. All the very best for your future endeavors!