You could try, but that's gonna be a pretty comprimised setup. The Vandies are designed for a minimum seating distance of 8'. Any closer and the drivers don't blend the way that they're supposed to. With 12' of space, you're looking at placing the speakers 2' away from the front wall and you sitting 2' away from the back wall.
I don't know your exact room layout, but placing the vandies along the short wall may be an option. Perhaps placing them about 7' apart and sitting the minimum 8' away? You would probably need to toe in the speakers just a little bit, but Vandies don't seem to have as much trouble being placed close to side walls as some other speakers do.
Either way, in a room that size I would go with the 2CE Sigs, personally. Sure, the 3A's could work, but it just isn't enough space to do them justice, imo.