Have Amy and Shadow gone on a date

Officially, NO. Amy has never dated Shadow in any game, comic, or TV show, but she has gone on a few dates with Sonic. He's missed a few, like in Sonic and the Black Knight.

In fanfiction, Shadow and Amy have dated. And by fanfiction, I mean amateurish writing pieces submitted by 13-year-old girls with no taste in literature. (God, I sound so snooty, lol). ALL UNOFFICIAL. And totally out of character by the way. Shadow basically has no emotions. He's usually only sullen and angry. He never says he "loves Amy" and he never shows interest in her.

Amy is clearly in love with Sonic in the games and Sonic seems to return her affections in Sonic X and some other games. In the comics, Sonic loves Sally Acorn, but Amy still loves him.

You can make up your own stories with Shadow falling for Amy and dating her. Whatever floats your boat. ;) Shadow is pretty cute. <3