This actually true, from end of 19th century with Swami Vivekananda teaching the upper crust of pre-WW2 society, to Srila Prabhupada in the land of the hippies.
In the mid-60's, immigration was loosened for India nationals. along with others, Swami's and guru's came, saw, and conquered; at least in a small scale
Srila Prabhupada arrived in NYC in November of 66, and thus began the western Hare Krishna movement.

A story: I was visiting a Canadian friend in Vancouver BC about 1985. We were in queen Elizabeth Park where we heard and recognized the sound of mantra being chanted nearby. We wandered over and found a young monk of uncertain English but clearly vaishnava-ish.
As it happened we gave him a ride to his lodging, learning that he was here (near USA) by his Guru's wish.

By Guru's grace my Indian teacher expounds the Upanishads in good English. Now they all have zoom-kulams; internet technology to spread the word, and to discuss the disagreement about which word and what do words mean; and "who" is listening.
What to speak of learning.