Love indian culture and yoga. Can I ask an indian doctor at a us hospital to use some treatments from there to heal me of churg-strauss syndrome?

No. Churg-strauss is treated. It is not something that can be healed. You must not be foolish about this disorder. Trying unproven methods for treatment can endanger your life.
Go for it. I'm also a buff of classic East Indian thought. Use the Ayur-Veda and whatever else but only as adjuncts -- if you cherish your life. Churg-Strauss is lethal if not treated by today's evidence-based medicines. As a med student, I kept Vivekananda's "Karma Yoga" on my desk ("I've got a right and a duty to work for a world that owes me nothing.") Best wishes.
You can ask. But the doctor will likely convince you to use western treatments. Physicians who come to the United States to complete training in U.S. Hospitals are taught western medicine. They make really good western physicians. More and more health care in india is based on western methods & western medications. You are looking for an ayurvedic-trained physician who may or may not be indian in origin.