Only if by cultural affinity you meant a Caste system had Tibet had any similarity to India. Buddhism was wiped, or in your word cultrually-genocided, by Hindu

Only if by cultural affinity you meant a Caste system had Tibet had any similarity to India. Buddhism was wiped, or in your word cultrually-genocided, by Hinduism already in India. The only reason why India might be anywhere interested in hosting a Buddhism monk is to annoy China, and nothing else.