Would SMS from the government, Facebook and the banks stop if a mobile number is registered under do not disturb in India?
Simple answer is NO.
Not at all. I am registered for the service, and I still get texts from essential services.
Bank transaction SMSes will not stop however Bank Promotional SMSes will stop. Will depend on the DND option chosen. Government is exempted from DND. Facebook, Twitter, etc. will not stop and these SMS options to your cellphone are explicitly defined and configured by you, so you are logically setting the permission to these websites.
The service also has two options to choose from -- 'Fully Blocked' or 'Partially Blocked' category. The first option puts a blanket ban on any commercial SMSes or calls. In the second, you can receive few SMSes like your important bank updates or traffic alerts, or the category you choose. The Partially Blocked category has identified eight options -- banking and financial products, real estate, education, health, consumer goods, automobiles, communication and entertainment, tourism and leisure -- for the users to choose from. If you register for the first option you will not receive any commercial communication.
No. SMSes from Facebook, Twitter, TxtWeb, banks and government (only in special cases like recently the case of NE students exodus) and some more services are exempted from DND. You will continue to receive messages. Besides, you can try DND for a week because now a days you can change your preference after 7 days.
However, SMSes from sms gateways like way2sms, 160by2 etc. will stop if you prefer for full DND.