You're thinking of Earth, where the polar ice builds up perpendicular to the sun, causing tidal effects to wobble our axis a bit. In this case, the ice is buil

You're thinking of Earth, where the polar ice builds up perpendicular to the sun, causing tidal effects to wobble our axis a bit. In this case, the ice is building up in such a way to make the planet even longer in the direction that tidal locking already had elongated it. The effect of which is that tidal locking would get stronger; not weaker. I don't think it matters too much that it'd be icy on one side and rocky on the other; I think it matters more that it's oblong. But even supposing it does matter, if your intuition is that the more-dense end would want to fall towards the star, then that'd be the rocky end; not the icy end. Yes, the icy end got heavier supposing you measure from the rocky planet's center. But if you shift your frame of reference to be the planet's center of mass, then both halves of course kept exactly 50% of the mass; the densities are what shifted.