To some extent, yes. Depends on the "City" or the area generally. I travel quite a bit so I do see this some. Metro areas Like Atlanta and all of Florida are losing the accent. In fact, in most areas of Florida, you would think you were talking to someone in Cali. The most unique accent was in pre-Katrina New Orleans. Natives there have an accent almost identical to a Brooklyn accent but a little less nasal and not as fast. Mississippi really doesn't have any large cities. But even in Jackson area you can see a bit of the drawl fade. But, we got guys that really talk like Larry the Cable Guy too. And some women who still sound like Scarlot O'Hara. I think the more rural the area, the more prominent the drawl. City dwellers tend to be clustered around more people who have moved to the South from other areas like northern and western states, and the melting pot effect seems to dissolve the drawl. I also think in the age of mass communication, cable tv, etc etc. the more we hear "normal" speech the more the coloquial speech disappears. Hope that answers that.
Rick