That may be the case for many people across the "Hindi belt" of northern India. (Hindi and Urdu, at an everyday level, being fairly close to a case of "same spoken language, different scripts".) In the Dravidian-speaking south....not so much.
No. People in the northern region would since it is similar to Hindi. Karnataka, Tamil Nadu and Kerala have their own language respectively which is different from Hindi and they wouldn't.
I am not certain about entire Andra and Telengana. People in Hyderabad speak Urdu.