Nothing in the ocean gets even close to the pressures required to result in high pressure variants of ice. Even the highest pressure of Challenger Deep is still an order of magnitude short of that.

The ice that forms at the point described (0 C and 1 GPa) would indeed be less that of water at the same point. It would be a mixture of Ice V and Ice VII, since that is the transition point. Neither of those forms of Ice naturally exist on Earth.

We do have a tiny amount of extremely high pressure Ice on Earth - specifically, Ice VII. It needs a much higher pressure to form than the water in the ocean can provide: thus far, we have found it in exactly one place on the planet (outside a lab) - tiny inclusions inside diamonds.