I think it could be a possibility, in thier chariots, some sources place Hittites as migrating out from the Maykop culture. When I watch the DVD which recreated their temples and walls, of massive thickness, and other things about them, it seems they were a HUGE culture, the ruins are massive, these people were really powerful and imo had the abilities and fit the mould of the people who entered India. Ramesses didn't win anything - the Hittites held their own against the most powerful nations of all in their time.
As I said, I believe their downfall may have been what generated the 'dark ages' at the end of Mycenaean culture - it makes aot of sense of you think about it - they were supplying everyone with horses and backing of all kinds, when they fell, it would only be logical thier allies would crumble if they weren't strong enough to support themselves, Mycenaean Greece had nothing to offer to sustain itself.
Your own link runs contrary to your idea in this matter, to whit:
Post-Harappan civilization 1900-1000 BC shows the abandonment of the Harappan towns owing to ecological and river changes but without a real break in the continuity of the culture. There is a decentralization and relocation in which the same basic agricultural and artistic traditions continue, along with a few significant urban sites like Dwaraka. This gradually develops into the Gangetic civilization of the first millennium BC, which is the classical civilization of ancient India, which retains its memory of its oRigin in the Sarasvati region through the Vedas.
The New Model