Actually I think why it works that way is it increases the amount of CO2 the must can hold so it absorbs the CO2 from the fruit which is what keeps it floating. It might float again once it was warmed up if there is still fermentation happening because it creates more CO2 that sticks to the fruit and makes it buoyant again, I had that happen this summer with the Sima I made for my in-laws.
As I see it after applying my brewing knowledge to the JAO recipe, the general rules that apply to JAO (that we usually determine with SG for any other batch) are:
When it clears, the yeast is done its job, is no longer active enough to wiggle around enough to stay in suspension and so it starts settling out. But they can still do their job from the bottom of the carboy, so you may still see bubbles rising from the lees from the few hardy yeast cells that may have a slightly higher alcohol tolerance than its parents and siblings.
When the fruit drops, it should be completely degassed and generally safe to bottle because the must has absorbed all the CO2 from the fruit and released it to the headspace, although I usually rack it and let it sit around for another month because I have had a few variations on JAO make bubbles after bottling.
By cold-crashing it, you artificially decrease yeast activity, which makes them drop out of suspension, but sometimes by warming them up they'll reactivate so it's best to rack off the sediment as soon as you plan to start warming the batch up again if you were planning to stabilize it so then there are fewer yeast cells for the chemicals to deal with so a better chance of the sulphites and sorbate working. But if you weren't going to stabilize, and the batch was actually done fermenting, the fruit should stay sunk because it'll be easier for the CO2 that becomes too much for the solution to hold to escape to the headspace rather than back into the fruit, unless fermentation kicks up again, in which case your fruit might well float again as more CO2 is produced. This is my conjecture, I could be incorrect and the CO2 may well use the fruit pieces as a nucleation point and cause it to float again briefly until it reaches an equilibrium once everything's warmed up, then it should sink again, like putting a raisin in a glass of ginger-ale, it will float for a while and then should sink once the carbonation's gone. Swirling it around to release any bubbles building on the fruit won't break the warranty any more than cold crashing or stabilizing it would.