Whether scooters are safe in India to travel on would solely depend on where you would be riding the scooter. Riding a scooter in Delhi or any other busy city should be avoided, the crowd is awful if it's pedestrians then no one is going to wait for you to pass, instead, they would jump in front of you to cross the road. With the road traffic, anyone would overtake you anytime regardless its the left or right side, cars, small tempos come really close during traffic times. It's like you would need eyes all around your head.
but the somewhere like Goa, Kerala, Shimla or Manali would be more convenient and safe.