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After Lyanna Mormont gave her speech and everyone started hooting-and-hollering, I'm not sure if anybody from the Vale (House Arryn) was voicing their agreement that Jon was the new King of the North.
Of course, the intentions of Lord Baelish are always unknown, but officially, is House Arryn:
declared as recognizing Jon as the new King of the North and ready to leave the easily defendable Vale and follow him into major combat?
declared as sympathetic to House Stark, but neutral? Going to war with any major army and risking major casualties will take convincing?
after Battle of the Bastards (BoB), the only remaining forces in the North are in the Vale? How many lesser Houses sat-out the BoB? It'd seem Jon has no army to command...
At end of season 6, does House Arryn 100% follow the King of the North? Or are they sympathetic but neutral?