Yes, Xion was created without an appearance, despite being a replica of another person, she's really just a vessel that has a duplicate of his powers, since he had no memories and things in KH are very heavily memory-based, blah blah. So technically she doesn't even have a gender. The face of the girl with black hair was taken from the memories she received artificially: Sora's. So she looks like Kairi, Sora's most important person, but with black hair instead of red. Since it's the first face she sees when she looks in a mirror, she thinks of it as hers.

Usually she will only appear as Sora or Roxas to those who know them well, but the canon itself is very vague as to what her full capabilities are. Hence the wildcard. Ultimately it's up to whoever wants to participate!

tl;dr Tenshi accepting her no matter how weird she is would probably be a huge boost for her self-esteem. :p