Sanskrit was written with all Indian scripts, whatever was in use in the region. I once read that the first book printed in Sanskrit used Bengali script - not sure about that. Only in the 19th century did it become common to use primarily Devanagari for it.
Some other languages of South Asia were also used, and later became their own nations (e.g. Sindhi), and only rarely do we consider them under the same umbrella. However, even for now most of these languages are spoken in the northern subcontinent — e.g. Persian, Uzbek, Kerry... So with this perspective of things, does Sanskrit really count as “India”? And if we look, what do we find ? First, let's look at this in terms of “dialects”: Bengali: “a native language of Bangladesh, but not as old or old-fashioned as Bengali itself”. (Bulk K. Kulhari) Sanskrit: “an Indian language based on Sanskrit” (Sivanandam Srivastava) Urdu: “a modern language that may be regarded as a dialect of Pashto, but is not the same as Urdu. “ (Manual Haiti) Punjabi (or Nathan): “a Punjabi language, speaking a different regional dialect from the rest of the Indian subcontinent. The modern spoken variety.