If an Irishman moved to Greece and learnt to speak Greek, would he still have an Irish accent?

The folk musician Ross Daly is of Irish descent, and has lived in Crete for 35 years:

He has a broad Cretan accent, and he has something non-Greek underneath it. But it’s subtle, and it’s not an Irish accent per se. At most, it’s a somewhat overcareful enunciation, and maybe, if you listen closely, some aspiration on his voiceless stops. (Which is English, of course.)