I have a feeling he’d let her, as well. Like, he’d make a BIG fuss about it (and Catelyn would flip her shit) because she’s a Stark of Winterfell and Gendry is just a bastard. But then Arya - being Arya - would do it anyway and Ned would forgive her, and accept him.
And, ugh, it would be beautiful. But it won’t ever happen because he’s dead and Arya is at the other end of the world to Gendry now.
(Source: thebullandthedirewolf, via em705)