

Nope.
That is, instead of sinking into the depths, surface water is being replaced by deep water masses rising to the surface, bringing with them heat and carbon dioxide (CO₂) that had been trapped for centuries.
I had to look up that last part, as it seemed counter-intuitive, but apparently deep ocean water bottoms out at 4 degrees C.
I’m not going to claim to fully understand the nuances, but the sea ice will melt at about -2C and glacial melt will deposit ~1C water into the system. If the deep water is steady at 3C or 4C, sending it up could accelerate melting of both.