Yes (to the title question), the sentence
User listed already having an attorney.
is valid. However it can only mean
[The] User included on a list already having an attorney.
[The] User placed herself in the category 'already having an attorney'.
That implies that the two alternatives (in the body of the question) have different meanings, because the second alternative means
The other 6 were rejected because [the] user is listed [by us, the company etc.] as already having an attorney.