All sorts of issues arise here, some of which have been mentioned. For instance, that Hinduism is monotheism is not correct. If we take the Baghavad Gita as definitive then Hinduism (as it came to be known) is an instance of the Perennial philosophy, advaita or 'nondualism'. The underlying metaphysic is explained by Nagarjuna without the use of zero as a concept.
I find the idea in the question profound and interesting. A good book on the topic is Robert Kaplan's The Nothing That Is: A History of Zero. For the most part it is a mathematical history going back to the early Indian use of zero, but the final chapter becomes metaphysical and here he makes a direct connection with Brahman when he suggest that the world may not be just more simple than we think but more simple than it would be possible for us to think - which is the claim of the Perennial philosophy. Another relevant book would be Spencer Brown's Laws of Form.
As a number zero cannot be associated with the formless. In mysticism the term 'advaita' (not-two) is used to avoid the suggestion of 'One' or 'Many' or any numerical value. Emptiness would not be zero but is also fullness. Unity is not a numerical 'Zero' or 'One' but encompasses multiplicity.
I wonder if the question works without introducing Buddhism. It seems highly likely that zero was introduced as both a mathematical and metaphysical concept, arising naturally in connection with metaphysical/religious issues and not just out of mathematical necessity. Buddhism rests on the metaphysics of the Upanishads so did not add any new ideas about nothingness. As I understand it it was the Vedic practices that had evolved through Brahmanism, (ascetism, animal sacrifice, over-respect for authority and so forth), that Buddhism was unhappy about.
What works against the idea of Buddhist influence is that zero plays no part in Buddhist metaphysics. Number and form would be part of the mundane world and zero would belong in this world. Metaphysically-speaking there would be no such thing as 'Nothing' if we mean nothing at all.
So while I can see how the use of zero might have been motivated by metaphysical considerations I can't see any need to suppose that the emergence of Buddhism had much to do with it.
The association of zero with identity is a profound issue that deserves a long essay. It relates to the 'thing-in-itself' of Kant. If we travel beyond number and form then all is identical (because of the identity of indiscernables - a point Kant seems to have missed). Thus where there is no distinction or division there are no 'things' and there is identity. This would be a state prior to zero since zero is the expression of a conceptual distinction (zero is not-one etc). That is, zero is a relative term meaningful only in the world of relativity. Mysticism often speaks of the 'Nothing' but this is not nothing at all, just an absence of things.
I'd recommend Kaplan's book. It's not a metaphysical discussion but the foundations of mathematics is the same topic in translation and he sees the connections. He carefully charts the origin and use of the term in Indian culture and beyond.