No. Because India already has several national languages. English is one of them. Hindi is also quite widely spoken, thanks to the influence of the Hindi cinema industry.
Languages cannot be imposed on populations. Well technically they can be imposed, but the outcome is good neither for the language, nor the people. The tongue in which people speak, grows and evolves into its status. It is a very organic process.
The debate about north vs south India, and the one about Hindi vs Tamil is a dead horse that some people are still flagellating because they never caught up. If you are someone who still sees some kind of tangible distinction between the north and the south, ask yourself why there is no such divide between the east and the west of India and why Gujaratis are not expected to speak Bengali?
The divide is bogus. The language issue is a non-issue.
I think English is an Indian language. It may not have been born here and it may not be the language that the Mughals or the Hindu kings used, but it is here now and it has been here for a long time. The person who asked this question knows and uses English. Everyone who answered also uses English.
In keeping with its inherently diverse nature, India should have as many “national” languages as it can. Linguistic diversity is a cultural advantage. We need to stop treating it as a handicap and wishing for a homogeneous single language that, like Sauron’s “one ring” in LoTR, will unite all Indians. This will not happen unless you make the conscious decision to devalue all existing native languages of India.