No, the game is set in the period from 500 B.C. to 1 B.C. and during that period firing while moving was not common. It could possibly be added for some types of high quality horse archers but isn't a high priority.
Even well before then the Scythians were known for their horse archer armies and were tricky to defeat.
I know it doesn't seem like a big thing, but if Romans can form testudos while moving, then it seems only fair to have true horse archers. Both so that players can accurately recreate the tactics (horse archers + heavy cavalry were the mainstay of several eastern factions which people might want to mod in) and just because they're more interesting that way. Otherwise the game's horse archers are little more than fast moving foot archers, which doesn't allow for much more creativity.