I don't think it is possible for warmer water to move up the water column while there is surface ice and/or the thermocline is able to form.
I have tried to find the original paper from Yale and failed so far. That said, I could have phrased that better. IIRC, the concern in the article was that the lower, warmer stratum was getting warmer and thicker and the upper layer was getting warmer, thinner and saltier.
I find thermoclines/haloclines somewhat magical by their ability to stay separate, but, AFAIK, it comes down to density. My impression was that once the ice goes, there is a relatively small volume of water hovering around freezing that will be heated up quickly.
If the upper layer increases in temperature and salinity, due to ice loss, then a merging of the two could occur. Understanding the exact process is above my pay grade, but the takeaway was that this shift would seriously affect/delay ice formation in the fall.
If anyone has more info on the situation I'd be happy to read it.