At one point in the film, Moe and Noodles both watch a TV news report about Senator Bailey don't they? Moe doesn't say anything, so I take from that that he doesn't know Bailey is Deborah's partner. I can believe that - siblings can grow apart quite a lot, it seemed like he hadn't spoken to her in years, so he might not know who she's connected with, and even if he has some idea she has a partner, might not know it is Bailey/Max.
No, sorry. I don't buy that.If you have a celebrity sister, people are going to ask you about her. Moe still works right there in the old neighborhood; the movie gossip magazine goes back well before 1968. Friend of a friend, the word gets around. The people in a neighborhood like that like nothing better than to talk about the famous people who used to live in their midst, and by posting nostalgic pictures of Deborah and the old gang at his bar, Moe certainly does nothing to discourage this. A Cabinet Secretary shacking up with a movie star would still be newsworthy today (remember Sen. Bob Kerrey of Nebraska and Linda Ronstadt?) -- it would have been scandalous in the 50's and 60's.Incidentally, that TV news report about Secretary (not Senator) Bailey would at least have featured a stock photo of the man.
People are strange, and families can be wierder, some times there's bad blood between siblings and they couldn't care less about the well being or the whereabouts of each other, just as if they are already dead and buried, I've run into these situations in various families. It is possible.