Is there a chance of Kugane becoming a "instance is full?"

[Risvertasashi]

Picture this scenario:
you'll do everything, get a queue of 120, get excited cause you''ll be one of the first 600 in who get a house, then BAM "instance is full" and the game exits, you log back in and you're 4,521 in queue

It's very possible. Keep in mind the difference between #200 in the queue and #4000 in the queue will (as you seem to have surmised) be but a few seconds.

whether the instance is full, if that will happen... will likely depend on just how early you get logged in. But I would worry about queue first. Even a few seconds late is likely too late either way.