I don't think the Karmapa Ogyen Trinley cares if the Indian government recognises him or not. If he is after fame, power and money, he would not have run away from the CTA and met up with the Karmapa Thaye Dorje. Meeting up with the other Karmapa could mean that they have to decide who will be the throne holder.
From the video that was once released by the Karmapa Ogyen Trinley, he sounded very sincere when he said he does not want to get involved in politics and he only wants to spread Dharma. He was very unhappy in India because he could not get the education that he wants and do the things that he wants. He could be seen as ungrateful but I think he is compassionate in the sense that spreading Dharma is more important than the fame, power, and money the CTA can give him.
But anyway, the recognition from the Indian government is not important, they don't have the authority to do that. The Karmapa has no intention to go back to India and to be controlled by the CTA anymore. Now he has the freedom to do what he wants. The CTA has lost an influential high lama, their position is very shaky now.