Richard,
Yes, that was the steerage promenade. One tidbit (whether fact or legend) relates to 3C survivor Eugene Peter Daly who, as the Titanic headed out to sea, played his farewell to his home Ireland on his bagpipes while on the Stern. The area was loaded with benches on which people could sit and relax.
As for who were allowed there, obviously the steerage and crew. Although the space wasn't designated for them, 1C might have had access. Those with money tended to have certain . . . privileges over those who didn't. I wouldn't say that 1C had spent time on the stern at any time during the voyage, as none were likely to have wanted to do so. That would have put them mingling with 3C, which, at that time, wasn't done.
If you are thinking of placing figures anywhere on the poop deck, the steerage will not cast your work in error.
Good luck!