Short and sweet (well sour) answer: don't know.
I tried the same 'fudge' with my UK NHS certificate, which generated a QR code on the French pass, but the Italian covid checker app refused it. It seems that the code generated by the French app for these 'overseas' certificates is not quite the EU one. Go figure.
The ministry of health promised and swore that they'll release more info by the end of the current month - i.e. tomorrow. Knowing them, and based on what they did in the past, this will happen at 16.59 tomorrow afternoon. Unfortunately these measures are done on very short notice... which is frustrating.