Well, McGivers' exact words were, "From the northern India area, I'd guess... probably a Sikh." So yes, she assumes he is Indian. And by extension, we as the audience are supposed to take this dialog at face value and assume the same thing.Nobody ever said Khan was Indian, to be sure. A Sikh, yes - if we are to trust Lt McGivers, who would have been motivated to deceive our heroes. Her claim of "probably a Sikh" is never ever repeated elsewhere in Trek...
That Cumberbatch and Montalban look nothing alike is the source of concern here (dodged by "Agent Harrison must have worn three dozen faces on his missions"), not any firm knowledge of who Khan must or must not be.
Timo Saloniemi
As far as his particular ethno-religious background, he has the longer hair, but doesn't have other identifiable traditional Sikh accoutrements such as turban, beard, and metal bracelet. So her additional assumption about him "probably" being a Sikh, based on looking at him in the sleeping chamber for five seconds, seems to be a stretch from a real-world perspective. We do find out later that he has the name Singh. But, while all male Sikh initiates have the surname Singh, there are also non-Sikhs who have the name.
Of course, it was basically a throwaway line to give the character an "exotic" air for the typical American casual viewing audience of the day, who was not sitting there with a pile of reference materials (or the internet at their fingertips) ready to fact-check and nitpick stuff like this like we are doing fifty years later.
Kor