Re: overcoming the head:
Yes, much as you have to overcome the battery bank voltage before you can start charging it. I imagine the same is true of a positive-displacement pump: if you don't have the wind to move the piston against the force of the head, you can't complete a single stroke. But the length (or rather shortness) of the cam or crank is used to trade volume for force, so even a light wind can keep pumping.
I guess the equivalent for a centrifugal pump would be using a really small one, designed for high pressure, low volume. It would never shift huge volumes, even in a high wind, but the bladeset could keep turning it even in low winds, raising a small volume to the required pressure.
But a continuous-use application like a heat pump doesn't really have a head.
It looks as though you are not proposing to use an intermediate electrical stage so you have a few interesting mechanical problems to tackle.
Heh! I've just had a vision of a 'mill with two hosepipes running up to it, twisted around the tower
I was imagining it used with a VAWT, so I hadn't even considered the rotating linkage to connect hoses to a HAWT.
And yes, no intermediate electrical stage. Much cheaper with no magnets or copper, and it would surely be reliable - heating and/or cooling, with only one moving part (the bladeset right through to the compressor stages, all on one shaft).