Usually when we talk about speech recognizers and accents the focus of the discussion is about how a strong accent impacts the accuracy of the result. And of course it does. Let's not forget that the earliest research and development for speech recognition was done in labs where the researchers provided their own speech samples. And it shouldn't be a surprise that most of those researchers were males with academically precise accents. In fact up until the last five or 10 years recognizing speech from adult females (even with very standard Midwestern accents) was significantly less accurate.
Researchers at Dartmouth have made some advances with algorithms to detect and parameterize some of the components of dialect. The researchers, who are socio-phoneticians, focused their approach on the differences in vowel sounds from different regions. Some earlier work done at the University of Pennsylvania described a batch process that can automatically align some of the speech parameters with the transcript. (FAVE: Forced Alignment & Vowel Extraction).
Regarding this newer work DARLA co-developer Jim Stanford said "Fully automated vowel extraction methods still have a long way to go, but as ASR technologies continue to improve, we believe the DARLA system will be useful for more and more sociolinguistic research questions".
Who knows? Maybe someday soon when somebody with a Georgia accent speaks with a virtual agent that agent may automatically respond with "how y'all doing?"