Puntosaurus, i have wondered the same thing about the change of lift vector in an unbounded wing in a wind tunnel. I'll just consider this, rather than rewrite Waspy's excellent post.
Basically in all flight conditions the induced drag is always the result of the angle of attack revectoring lift rearwards. Don't forget AOA is defined from the datum of tip to tail, so even a cambered aerofoil will produce no lift at zero AOA (they will be optimised for say 8'). Put another way zero AOA can be defined as the attitude of the wing section to produce no lift.
When the wing section is in a wind tunnel, increasing the AOA both increases the lift vector magnitude (since Cd increases with AOA) and revectors it rearwards. The drag is thus the result of the induced drag, and a parasitic term associated with the increasing turbulence as you approach stall. If the same wing section is operating in free air the tips spill off the circulation as vortices. These vortices mean that the section is now effectively operating in a local downwash. Thus the AOA must be increased a little more, to produce the same lift, and thus the induced drag goes up some more.
So yes, if you had no tip vortices an aerodynamicist would still say that there is induced drag on a lift producing wing.