How do you think the Blackfish would treat Arya? Let's say in some AU, Arya makes it to Riverrun, for argument's sake Cat is gone (either post-RW or on her way there), and the Blackfish takes her in to protect her. Brynden will quickly learn Arya isn't a "proper highborn lady", but given the type of person he is and how he treated Cat/Lysa/Edmure/LF, do you think he'd encourage Arya's "needlework" or martial desires? It's still possible they meet up at some point, so we could see this for real.
Aww, it warms my heart to imagine this, because I think they’d be extremely fond of each other; the Blackfish would immediately recognize a fellow black sheep, and I can easily imagine him continuing her sword training and her making him howl with laughter.