Hmm. I think that's different.
The Irish woman _meant_ to say "doesn't" as in "does not". Whereas, "gone" is a phonetic false cognate of a contraction of an abbreviation...
The locals didn't _mean_ "gone", they meant "going to" >> "gonna" >> "gonn'". So the writer of the Alabama town should probably have written "Not gonn' eat with me?" instead.
The key difference being that, for reading, it is harder to understand "She gone have to beat em away" than "She gonn' have to beat em away" because the former puts in a recognisable term that is incorrect and has to checked and then corrected in the head whereas the latter puts in an unrecognised term that only needs to be checked once and can then be recognised every subsequent occasion.
G