Hi Flaperon75,
Would the arrival airport drop out as I fly over the threshold?
It depends on the software Mod of your FMGCs.
What you described is what we now call a discontinued approach. Our FMGCs will sequence the GA procedure, but we would have to re-enter the Approach for the runway again.
Older FMGCs will loose the GA procedure unless you selected TOGA briefly.
FCTM Page 198 (NO-170 P 2/4) gives some advice:
"If TOGA thrust is not required during a go-around for any reason, e.g. an early go-around ordered by ATC, it is essential that thrust levers are set momentarily but without delay, to the TOGA detent, the full forward thrust levers position, to ensure proper go-around (SRS/NAV) mode activation, and to sequence the F-PLN."
With older FMGCs, you could select TOGA briefly to sequence the flight plan, then retard the TLs to approach power (so aircraft doesn't climb at SRS speed), pull VS (select say -700ft/min), check for "Speed" mode, restore TLs to climb gate.
Or some other acceptable method.