Not exactly.
There's been a brain drain among states where abortion has been banned. People not enrolling in medical schools and also vacating medical jobs in them and heading off to other states. The specter of whatever future changes in laws affecting medicine is it is succeeding and scaring them away.
The general backward climate and other such moves is also helping to chase away more educated types. Just look at a state like Florida, known for rapid population growth. Except that 500,000 people have left the state in recent years.