I think it is possible that someone can be a survivor of sexual trauma and still be asexual. I doubt the two are mutually exclusive. I would guess that the difference between no desire due to trauma and no desire because one is asexual would be whether or not the person with the traumatic background has worked through their issues.

Also, I wonder, is being asexual sort of like being gay in that one is born that way or is it possible that one could have enjoyed sex at some point in their life and then later lost interest? To be clear, I would be speaking of people who are not going through any medical issues, dealing with trauma, hormonal changes, or excessive stress. People who are healthy, hormones balanced, and doing well in life.