No. The Admiral who recruited all of us is named Poseidon, but I'm fairly certain he isn't the same one.
Magic is a lot more random there than it is at most worlds I've been too. Mount Weather might give it a run for its money, but that's because there the radiation outside interfered with most magic. In Atlantis it seems to be more playful, if that's the right word. I'd say random, but we haven't had playing cards rain from the sky yet. I think that was the most random thing I've experienced.
No one was in Mount Weather by choice, either. That is, we didn't choose to come, but we couldn't choose to leave, either. No one had determined exactly why we were brought there. In Atlantis, there's always the option to go back after one's first week.