Well, my apologies for having the conversation go opaque.
I think at 100% coverage, in the centre of the cyclone (low wind speed), and with thick ice your statement is definitely true.
At relatively thin ice, when it is broken, and at larger wind speeds the effect appears to reverse, because the turning angle of ice drift gets smaller than the turning angle of the wind (compared to the isobars).
I agree that we have seen declining concentrations under the centres of (weak) cyclones, but the above would also reason why, despite the stronger winds and breaking up, I am not aware of strongly lowering concentrations in the regions of higher wind speeds, where in a naive picture one would expect the largest effect.
So, to make my naive picture: If we have a relatively round storm with a wind maximum, the ice should have a net divergence in the centre, a less divergent (and probably convergent) region around the wind maximum and then increasing divergence again at the outskirts. That would thin the ice in the very centre, thicken inwards of the max wind radius, thin it in the outskirts (and relatively far in, due to the radial drift differential).