No. "Invisible" makes you appear offline to everyone else, but people still see the messages you send, and anyone in a voice channel sees you when you join it.
Does "Invisible" hide me completely on Fluxer?
No. "Invisible" makes you appear offline to everyone else on every device you're signed in on, and it hides your custom status too. People still see the messages you send, and anyone in a voice channel sees you when you join it, even while you're invisible.