A major point of discussion during season seven is that the North doesn't take kindly to foreigners demanding loyalty . . . so when Jon returns home with a foreign queen whose father killed many of the Northern lords' families during Robert's Rebellion, her obsession with ruling Westeros isn't likely to go over well.
The North stands behind Jon Snow as King in the North, so perhaps they'll take his faith in Daenerys as a good sign; but we don't envision the region accepting a Targaryen queen without a fight. Dany will have to prove herself to the Northern lords and ladies in battle, not simply through her "claim."