I doubt whether they would have the resources to track the other a/c to it's destination and discover it's call-sign.
Depends on where it goes, if it stayed high level then it probably stayed in radar coverage; otherwise it will disappear into the ether...
The ASA safety guys love these ones, if they are allowed to go looking. They might find it from departure rather than arrival. But to what end, to discover the wrong mode C or to give the pilot a kick in the you know where?
The ATSB might be more interested and can 'requisition' the tapes from ASA if they choose to do so. Look for CAIR, (Repcon) I think it's called now, as a way of dobbing him/her in.