It is possible for an English speaker to learn this unique style of singing.
The series of photos show a British woman, who is an English speaker, engaging two such singers in an impromptu lesson. Neither speaks the other's language and the instruction is done via body language and imitation.
The bottom photo shows the sound being reproduced by the Brit (on the right). Although a beginner, the fundamental learning process has taken place.
The scenes are in https://en.wikipedia.org/wiki/Ulaanbaatar.
For those wanting a practice lesson from the comfort of home, check out Khoomii (throat singing) lesson by Sundui
For those planning to learn on a visit, the best place to meet and engage someone to teach is at the Naadam Festival, where there are throat singing competitions.
Update 30 Sept 2015
I have now watched the film "Genghis Blues", which documents the travel by Paul Pena to Mongolia for the purpose of learning 'throat singing'. While it's true he eventually acquired a working knowledge of the language after a long time, when he first arrived and started learning his knowledge was limited to a few serviceable phrases of the sort that any traveller could pick up from a generic phrase book.