I can see Ducky knowing about Immortals, and I can certainly see him being acquainted with any number of them whether or not he knows that they're immortals, but I can't see him being part of a secret society that tracks them and/or helps hide their existence from forensic studies. He's too quirky to fit into that kind of society and he's too good at what he does for them to have let him go rather than study the bodies they retrieve.

Although I suppose if he were following someone around or just being sent to where he was needed for "special" autopsies that could explain some of his travels.