For those not qualified on 320/330/340. The manufacturers SOP and checklist requires that doors be checked closed before proceeding to eng start. The "DOORS" page is not inhibited as suggested but is replaced by the "ENG" page when "IGN START" is selected. To start pushback without checking doors closed is a breakdown in cockpit procedures. Maybe QF will need to look at their procedures. Some years ago I observed potentially the same occurence with one of their 747's departing Singapore. Fortunately on that occasion the bridge was retracted.
As for the comment from "bulkhead" about flying with a slide deployed - I think not. The ECAM in the cockpit would be making all sorts of noises etc. The PIMs in the cabin will also be giving indications and besides with a slide deployed the door will not close. Therefore, I will call you "liar" as you seem to be demanding.
Have a nice day