If you want to fly on the NAT tracks across the atlantic you have to be CPDLC equipped. This rule came in a year or so ago. (CPDLC is a more sophisticated version of ADS position reporting.)
An atlantic waypoint of say 53 degrees North, 30 degrees West is encoded in the FMS as 5320N. Without the database covering the atlantic you can construct the waypoint using lat and long but it would have a different appearance in the FMS (remember the early FMS "Green Goddess" atlantic waypoints of Wpt 01, 02 etc?) and the position report would not be recognised by Shanwick/Gander. Therefore the CPDLC data would not be valid and the aircraft would not be CPDLC compliant. So that means no atlantic crossing unless you go above or below the NAT tracks and I doubt the Airbus would have the performance or fuel capability to do that.