Yes, you can definitely participate in State counselling for NEET UG without participating in All India Counselling.

• All India Quota (AIQ) Counselling: This is conducted by the Medical Counselling Committee (MCC) for 15% of the MBBS/BDS seats in government colleges and all seats in central universities and Deemed Universities.
  
  
• State Quota Counselling: This is conducted by the respective state authorities for the remaining 85% of the MBBS/BDS seats in government colleges and private medical colleges within the state.
  
  Participation in one is not dependent on the other. You can choose to participate in either, both, or neither depending on your preference and eligibility (state domicile for State Counselling).
  
  https://medicine.careers360.com/download/ebooks/neet-aakash-national-talent-hunt-exam-preparation-kit-class-11
  
  I hope it helps!