So I actually tried this: I scanned an English NHS vaccination code into the Irish "Covid Tracker" app and into the French "TAC" app. The result looks like an EU DCC and seems to behave like an EU DCC. However, when you scan the converted French QR code or the converted Irish QR code with another EU country's checker app, their apps detect that there is something wrong with these converted QR codes. I used the German, Portuguese, and Luxemburg checking apps.
German: Certificate does not have a valid signature.
Portugal: Error emissor. Desconhecido. Invalid.
Luxembourg: Trusted repository not found.
None of these error messages occur when the apps scan a genuine EU DCC issued by another EU country.
FWIW. My guess it that whatever Ireland and France do in the way of conversion of non-EU certificates, it is only good for their domestic markets. So far the EU Commission has only recognised equivalence of COVID-19 certificates issued by these non-EU countries: Switzerland, San Marino, Vatican City State, Turkey, Ukraine and North Macedonia, and they will be connected to the EU trust framework, whatever that means. Yes, I know, this is a motley crew.