I also think
Sam's numbered comments has it about right.
We know something about parts of the Arctic that are largely ice-free which used to be mostly ice-covered (e.g., Bering being ice-free almost year-round a couple years, or Beaufort seasonally). Areas that are far removed from the current perennially ice-covered areas give us some clues as to what will happen in the central CAB when it becomes seasonally ice-free. The water heating up in some areas has virtually no interaction with late-season ice, for example, so we have some actual data. Sea water looses a great deal of heat during the Arctic winter; there may be some year-to-year 'memory', but not a lot of it (yet). Delayed freezing causes a little less ice growth, but charts show that thicker ice is the bigger damper on further ice growth, not time.
So far, we have not observed the total destruction of the halocline (maybe some?) anywhere. Therefore, I would not expect its destruction after the first BOE. At some point, yes, but not right away.
North Greenland will still be ice-covered after the first several (hundred) BOEs. Will it have a damping affect on the Arctic that will make some types of changes less extreme?
I contend the climate disasters humanity is experiencing are AGW-caused, and they will get worse as CO2e increases. Reduced Arctic ice cover (both area percentage and days/year ice-free), increased ocean acidification, and land use/abuse (deforestation, rice paddies, etc.) are among other elements that will amplify CO2e-caused climate disruption. The first BOE (by any definition) will not be a trigger for any global transition, unless, maybe, the first BOE occurs in July (giving 3-months of new conditions, but even then, the BO
event won't be the trigger, but the 3 months of added heat or open water will be). The transitions are happening before our eyes and are coming faster and faster. A BOE, just like 400 ppm CO2, is a statistic that points towards the Hell we are creating.