If DOS2 is any indication, yes, all Origin character should be open to join (max of three, of course, not including the main character). Additionally, there should be an option to have non-Origin characters join (as it was in DOS2). Again, only going by DOS2.
Should certain Origin characters object to other Origin characters and refuse to join? That would be a cool dynamic (or make them hostile to each other if they were in the same party).