Her intial opinion may not matter that much if she encounters them midway through a battle between Stark forces and freakin' ice zombies. The Stark would be unlikely to raise much of a fuss if they get desperate enough to do anything for some dragon fire, and it's hard to see Dany being hostile towards an opponent who's entangled in a magic war.
Of course, I kind of feel like our four main political Starks all have some kind of immediate counter to Dany's immediate righteous anger just because of their circumstances. Unlike the other houses, the Stark's don't have the traditional old patriarch or matriarch to be targeted by Dany. At the very least, their individual stories are all intriguing enough to slow her down if they meet her.
Sansa: "Your highness, I believe you know what it's like to be traded like meat to monsters, yes? I was gift wrapped for two seperate serial killers. How was your marriage?"
Bran: "I am contacting you through my magic control of ancient tree-powers. I'd meet you in person, but I regret to say my young body is crippled, which I'm sure has no impact on your sympathy at all."
Arya: "I can wear your face!"
Jon: "Two things: One, I've already died, and two, freakin' ice zombies."