In the profession of Doctors, it doesn't really matter from where you are studying MBBS and other higher studies. All that matters is your skills. If you are skillfull and complete the mandatory internship from a MCI or any state council approved medical college you'll earn the license and can run your own clinic and can also get jobs in various private as well as government Medical hospitals. You can surely do MBBS from a Private institution and then go for higher studies and based on the entrance score will be allotted a medical college. And while getting into a job in a hospital, the superior might ask you the question, so have to ready with answers. If your university is recognized medical college by MCI or other equivalent council then after clearing examination for government doctor you can easily be a government doctor in government hospitals.