Generally not as fresh milk, but cultured. Fresh milk tends not to last very long in hot climates without refrigeration, while forms like yogurt last much better.

There are lots of dairy products in Indian food, so, yes there's plenty of cultured ones like yoghourt & paneer ("cheese"), but significant numbers of Indians drink fresh milk (actually fresh milk - as in milked that day). When the Indian cricketer M.S. Dhoni was younger and was just coming into the lime light, there was an interview with him where the interviewer asked him his 'secret' and he said it he was drinking a glass of milk every day (or two glasses or something).