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.
or
[The] User placed herself in the category 'already having an attorney'.
See http://www.merriam-webster.com/dictionary/list.
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.