The funny thing is, North gaining independence would lead into a spiral of kingdoms abandoning the unified realm. Ironborns rebelled twice for that. I can't buy accepting North leaving and them staying part of the realm. At best, after Yara, i could see Ironborns cutting all connection with the other kingdoms. Also,it's the problem of the culture. The North could be a peaceful kingdom or cooperate with the others, especially now that House Stark controls all Westeros. Ironborn' culture is one of looting and raiding. Yara could keep the Islands peaceful, especially after the destruction of the Iron Fleet, but after rebuilding their navy, i could see them back to their old ways.