YES!!! You can play Batman: Arkham City in the Batman Beyond suit!
I had no idea about this DLC until I stumbled upon it while looking at the Robin DLC so Im spreading the news just incase you were living in a box like me and somehow missed this Awesome News?!?!
Screenshot picture taken by me but its all thanks to this amazing game: [link]
Batman: Arkham City [link]
Batman Beyond [link]
DLC Trailer [link]