No.
This is a terrible idea and I am an Indian, there's no such thing as greater India, except for in the minds of right wing nutters. Anyhow, Burma, Ceylon have never been part of any non colonial Indian polity even during British rule almost 40% of subcontinent was ruled by various kings/princes although as puppets of British empire.
Although Greater India can extend towards all of South East Asia and even Indonesia in more crazy versions.
I actually believe Hindus have been incredibly restrained given their pent-up rage after centuries of Muslim rule
lol. There was no clear Hindu Muslim divide in Mughal era, once again right wing nutters twisting history to present as this era to be some sort of colonialism on par with British empire, its absurd.
In India, remember "Caste trumps all", most of the Muslims were still living as untouchables or lower castes in Indian villages (which still can be seen in many rural areas) during the so called Muslim rule, imagine such treatment handed to Brits.
I also love how no one talks about the brutal raids of Marathas on the territories of Bihar and Bengal or the Punjabis fighting against dirty 'poorvaiyaas' (people from east) because there is no potential political capital out of these historical narratives as there is in some Hindu king fighting Muslim king.