In Georgia can a municipal police officer, still in his official cruiser, but outside of the his municipality's limits, pull you over for speeding?
Usually not, although there are a web of state and local laws that would depend a fair amount on the true jurisdiction of the officer. I wouldn't be surprised to learn, for example, that some law enforcement officers have county-wide jurisdiction even though they are paid mostly to enforce laws in a particular locality within a county.
There is a "hot pursuit" exception that applies for some offenses. I doubt that speeding would come in that category (particularly if it is a traffic offense rather than a misdemeanor). But, reckless and drunk driving might qualify for a "hot pursuit" exception. Also, importantly, pursuit to arrest for failure to stop for an officer pulling you over if the initial stop was initiated within the jurisdiction would likewise also qualify for the "hot pursuit" exception.
Beyond the "hot pursuit" exception, there are a variety of offenses which a uniformed officer could still make a citizens arrest for outside his jurisdiction, although speeding would probably not be one of them.