No, they do not get that info, the duke is supposed to be a help to the civilians not the mafia.
I think I need to tell the story of Thomas, the evil Duke, so here it is: The last time we had a duke, the person leading the game sent out group PMs rather than individual ones, so using those we were able to figure out who the majority of the civilians were. When we discovered that LOL was the sherrif and that she found out that Twilight was mafia, we sent PMs out to everybody who we knew had gotten a civilian PM. Thomas had gotten both and so he was part of the PM chain that was told that Twilight was mafia. To make a long story shorter, every time that we tried to hang her before she died, Thomas saved her.