Absolutely not.
The 14th Amendment’s language was derived from the 1866 Civil Rights Act, which provided that “all persons born in the United States, and not subject to any foreign power” would be considered citizens. Nimrata and her parents were all subject to laws of India, not the United States.
American Indians and their children did not become citizens until Congress passed the Indian Citizenship Act of 1924. There would have been no need to pass such legislation if the 14th Amendment extended citizenship to every person born in America, no matter what the circumstances of their birth, and no matter who their parents are.
The problem with your position is that unless Haley’s parents registered her birth with the Indian government, she was never an Indian citizen and thus, born in the United States and not subject to any foreign power. India does not automatically confer citizenship upon the children of their citizens that are born abroad unless they are diplomats.
American Indians are not a good analogy, as they were considered separate sovereigns and not subject to the law of the USA within the confines of their reservations. So until that law was passed, any child born on a reservation was considered to have been born in a foreign country.