I dunno.
I'm first generation Australian, thick Aussie accent and can speak nothing but English. My father, though, is Hungarian. He's been living here since he was 19, coming as a refugee in 1956. He speaks English only now and very well - in fact, he'd now struggle to speak his original tongue - but could never lose his accent.
It still cuts him up when people make fun of it. Like there's something he could do about it.
But hey, it's just a bit of fun, innit?