"a self- confessed muderer', yes. "a self-confessed serial killer'.
"a self-confessed swindler" " a self-confessed thief" "a self-confessed plagiarist"
If someone confesses to a bank robberery, or to being a jewel thief etc., he would simply be called so - a bank robber, a jewel thief etc.
It is also used humourously:
"a self-confessed chocolate addict".
Somewhat more seriously, Michael Douglas is "a self-confessed sex addict" that caused a divorce (or was it two?).
I read an article a few years ago about Michael Douglas and his so-called addiction. The article said that it was a false story about him. Before being married with Zeta-Jones, he had had only one wife. The article said that he is actually a family man. I think it's one more myth about one more celebrity but I really don't know.
Another actor who seems to have been infamously labeled by the media is Adam West, that actor who portrayed Batman in the famous television series. For many years, I thought that he and Burt Yard (Robin) were a gay couple in real life. I watched a show about his biography on TV a few years ago and, according to it, he has never had a homosexual life. Once again, I really don't know.
Not a couple? That's not the half of it.
Read Burt Ward's autobiography. The only way they could have been a couple is in a long-distance SM relationship, the way West purportedly treated him with disdain.
But who knows the truth of these matters?
My example was to show the truth of language -'self-confessed sex-addict' as an expression exists in the language.