Hi there. Yes, transmog will allow you to use ANY armor set you have acquired. You will earn materials through Ada-1 to change a piece of gear Into a universal ornament. Any and all armor sets will work, this includes your black armory and raids sets that you want.
I think it basically allows you to sacrifice old legendary armor you have to turn it into an ornament. Don't take my word for it though, I'm not completely sure how it works myself.