I didn't think this was possible but apparently i might be wrong...http://www.wired.com/magazine/2011/02/ff_fasterthanwind/
Truly amazing stuff, while this has been used with land yachts i see no reason why it could not be used on water with a prop or modified mirage drive.
I think there could be some improvements using the thrust of a mirage drive mechanism tied to the power from the sail but I doubt a TI could go directly downwind faster than the wind due to too much drag and coupling inefficiencies in water compared to a land sailing craft. But it is fun to explore some possibilities.
Imagine a vertical windmill in the mast slot of the TI with two drive belts connecting a wheel on each side mounted between the hull and amas and those wheels driving submerged flexible flippers on each side creating forward thrust like sculling oars. Since vertical windmills spin regardless of wind direction you could sail in any direction. But I doubt it would go faster than a normal TI due to drag from half the surface of the windmill (half of area of vertical windmill going into the wind) so nothing really gained.
If used a large horizontal propeller in the air on a hydrofoil sailboat then perhaps the drag would be low enough to go directly downwind perhaps faster than the wind provided you used some external power (only initially) to get it up on the foils. The trick would be to transmit a submerged propeller's energy to the air propeller above such that it rotated not as a windmill absorbing energy but in the opposite direction providing forward lift. But I would expect it wouldn't work because the losses coupling the submerged prop to the air prop would be much greater than the wheels coupling the air prop on the land vehicle though all other physics principles would apply.
It also probably wouldn't work for the iceboat version of a TI since difficult to transmit energy from the relative motion of the ice to the air prop - in that case due to too low friction with the ice.
It is possible to make a TI version that could go directly into the wind using a horizontal air prop but it would not be practical due to the danger of the spinning prop and it would probably go much slower than a normal stationary sail TI so would lose any upwind race.
However, there may be some improvements in the speed of the conventional sail TI in low wind conditions using the same principle of the thrust of the mirage type flippers if coupled to the energy of the conventional sail such that its angle oscillates slightly about its average optimum through a feedback loop from flipper propulsion.
You can test this flipper propulsion phenomena yourself now when sailing upwind in very light wind conditions by oscillating the rudder very slightly on an upwind tack and noticing the increased speed. The entire submerged TI boat surface seems to be acting like a sculling oar. Now just replace that tiny energy of your hand moving the rudder with the energy you use to hold the main sheet and imagine a flexible submerged flipper to amplify the thrust more efficiently and the motion of your hand replaced with an oscillation from a feedback loop powered through the force of the main sheet coupled through a pulley mechanism tied to a submerged flipper in one of the TI mirage drive wells.