Yes it can happen, however it will require you requesting and Airbnb contacting the guest to ask permission to ammend the review if it contains sensitive information that isnt applicable to the review process and future guests.
I had a guest who had the entire review I left her (she didnt leave one for me at all, however mine posted after 14 days) removed because I mentioned her guest by name and she didnt want any traces of her staying with her guest left anywhere on the web. (She told Airbnb it would cause problems for her if her family found out she was with this other person)
I suspect if you contact Airbnb and tell them the personal part of this review makes you very uncomfortable, they will start the process of contacting the guest to ask them to either delete or ammend the review.