Small electrical machines have a low efficiency, it is bad enough with the inevitable loss of one conversion when you want electricity. If you convert back to mechanical energy the losses make it a doubtful proposition.
Yes in theory the second machine would follow as a synchronous motor, but with high losses and no control of excitation ( hence power factor). Big sync motors are not very good natured and a small one would probably fall out of step very easily with gusting and compressor loading.
These things work best at fixed voltage and frequency, with raw ac performance would be poor. You would probably do better rectifying to dc and using an ECM dc motor, but matching the speed and load would still be a big issue.
Not impossible but a lot of work with many snags and only viable with a large set up.
You can't make up for losses with a few extra turns. I think you would be hard pushed to get 40% overall efficiency.
If you want to do it on a small scale you would be better off using wind to charge a battery to drive one of the Danfoss dc units, they are very effective for fridges, probably could be adapted to a heat pump. Probably a small battery would drive the pump and any excess power could be used for direct heat or as base heat for the heat pump.
Flux
