The question of singing in an assumed accent has no final answer because, as several people have come close to saying, the perception of "authenticity" depends entirely on who's listening. I used to think Ewan MacColl's Scottish pronunciations were absolutely authentic, but now I know that some Scots, at least, find them grating. Others don't, but still recognize that he wasn't "from around here." Americans, on the other hand, easily accept them - and worse.

The same is true of Southern Appalachian pronunciations. This distinctive accent (and variations of it) is very hard to imitate, but people who've never had much exposure to the real thing have fairly undemanding standards.

Ideally one should always sing in one's own voice, but if you really want to reproduce the song as you heard it, give it a try. Just pick your audience very carefully. Rule of thumb: If you're not Australian, don't sing Strine in Oz.