Greetings BOAC..
In an attempt to introduce clarity I offer the following to everyone...
Each pilot's FPV (bird) displays the track calculated by the onside IRS, and is subject to IRS errors which Airbus say may be up to ± 2°. When maintaining a track in manual flight you may therefore need to make a small correction in order to fly the required track.
When the AP is engaged as per the original question the AP uses the onside FMGC to fly the selected track (in the FCU window). I cannot find an FCOM reference but I assume this will be the updated value. The FPV will still display the onside IRS track. The a/c will maintain the track precisely - I reckon any observed error in following the radial is more likely to be due to VOR system errors than anything else.
Summary: the FPV may have errors, the AP will be very accurate.