According to Article I of the "Rehat Maryada" (the Sikh code of conduct and conventions), a Sikh is defined as "any human being who faithfully believes in One Immortal Being; ten Gurus, from Guru Nanak to Guru Gobind Singh; Guru Granth Sahib; the teachings of the ten Gurus and the baptism bequeathed by the tenth Guru; and who does not owe allegiance to any other religion". Sikhs believe in the equality of humankind, the concept of universal brotherhood and One Supreme transcendent and immanent God (Ik Onkar)
If that's the case, ethnicity doesn't enter into it. Anyone can be Sikh.
I'm thinking that Khan might be Sikh in name only.