Very likely they would, if their military leadership is completely under control and as fanatical as is usually assumed.
The rational assumption for those people is that NK is not a viable state without a friendly China, and with a hostile China it means the NK regime will be gone in short order. The question is - just how irrational are they?
That's the big unknown: I can see what the US wants (no NK nukes), I can even see the Chinese stirring things up with NK to cause trouble for the US, SK and Japan.
But what are the NK's getting out of this? The eight years of Obama's apology tour (and previous admin's flaccidity) convinced them that the US would do nothing. Now that it apears that we will (and may have the Chinese on our side), it's not clear how the NK's can climb down from the limb upon which they sit.
My guess is the only way to prevent NK having ICBM's with nukes is regime change in Pyongyang.