I don't know about separation anxiety, but I would think, after what you've said, that he associates people leaving the house with him being alone and hungry for long periods of time. Or something equally negative.
He may also have some misplaced ideas about what his job is, and be desperately trying to keep his pack together.
I'd think that creating positive linkages in his mind between people leaving and him being OK would help, such as -- have people put on their coats and reward him for sitting and being calm, and then work up to rewards when they leave and he stays calm, then have people leave and come back quickly and reward him for being calm, and so on. And do the whole leaving without a fuss business, too.
And somehow establish that the family is OK about people leaving, so he needs to be OK about it too, to relieve him of any ideas that he's supposed to be the one who keeps everyone together.
Best of luck to everyone. These stories are so inspiring -- I look forward to the time when I can be a furball foster home.