It may cause annoyance for others, but my opinion for what its worth is, if it feels right to you, then go for it.

Some songs don't feel right without an accent, fake or otherwise. I personally try not to sing in an American accent because it doesn't feel right, but feel ok singing with an Irish, Scottish or Welsh accent (relevant to the song) despite the fact I was born and raised in England. This is partly because I can trace my recent heritage to one degree or another to each of these countries.

Seems we may be getting back into the 'Is it Ethnic' debate of the early 60's.

Anything goes for me.