Yes, that's the joker in the pack. Did you see the papers about the evidence for the ice pack on Greenland having completely melted before? It left me wondering about how much we can trust the ice core readings from there.
Obviously it has all melted off before. Many, many times.
That does not mean anything is wrong with the current ice cores. It only means they go back only as far as they go, and there may be gaps where partial melting happened before accumulation resumed.
Tipping over into a new ice age would not be a better outcome than where we seem headed without that.
the issue in particular with the ice core melting is how much we can trust the peak readings for things like methane and co2.... what we consistently see in the cores is that these things increase steadily until they suddenly drop. If we are missing the top part of that information, it could be quite important.