Crazy as this looks, it would actually work. If the lift:drag ratios of the blades of the wind turbine and of the propellor were good enough, and the transmission from the turbine to the propellors efficient enough, it could even go faster than the wind in any direction except downwind*, which would inevitably be slower. The turbine can drive the propellors via shafts, gears, and perhaps chains; electrically; or even hydraulically – but whichever, it’s important that the efficiency of the transmission is very high!
At first sight, it looks as though it contravenes the law of the conservation of momentum when it’s going upwind, but like a conventional sailing boat beating upwind, it doesn’t do so: it tranfers more momentum from the wind to the water than it steals for itself.
Of course one might quibble about whether this is really sailing at all, but it is propelling a boat solely by wind.
If I was building such a boat, it would have solar panels as an additional source of power, and batteries so it could store energy when tied up or at anchor, for use later. But in the open sea, it’s not really a sensible alternative to a conventional sailing boat. You don’t need to sail directly upwind in the open sea, and this boat would be much more expensive to build and probably slower than beating upwind in a good boat, albeit probably easier to operate. The design might come into its own in restricted waters, such as rivers or canals – but clearance under bridges could be an issue. It gets more complicated (and expensive) if you have to consider being able to lower the turbine. There may be restrictions on the feasible diameter of the turbine, too, limiting the available power. You might design the blades to fold back parallel to the axis, but that complicates things yet further.
All in all, a fun idea rather than a serious proposition – as drawn. But a much smaller turbine (or two) and plenty of solar panels on a barge or narrowboat with a big battery and electric drive might make perfect sense, especially if you expected to spend much longer tied up than going anywhere (at about four knots, a sensible speed in a canal).
Back to Points of Sailing.
* Yes, I did mean downwind. That would very likely be its slowest direction, and certainly not its fastest.