The Badgers roost at the Black Tower Inn on the Street of Three Fishes. They will indeed allow you to join. Their Barkeep Marak welcomes you and assigns you a room in the Inn and gives you a tabard and an official seal. You are also required to swear the associates oath not to reveal the Company's secrets. The Badgers then send you to work and you learn that the Badgers part own and run Hunter's Inn and also have a hidden fortress on the southern coast of Maladon, called the Fortress of the Rock. You are sent there by ship and find it is a windswept Island that you passed on your way to Khulican. There you are put on guard duty and also help reconstruct a damaged section of wall. After a week you return to Haven and help man the towers at Hunter's Inn.