Can it partake of new wealth and still remain distinctly Southern?

When James Oglethorpe and his band established the first Georgia settlement in Savannah at 1733, theirs was the last colony, the one farthest down the Eastern Seaboard, a military buffer for the rest of the 13 colonies.

But as the Southeast has prospered, Georgia has been transformed from loneliest outpost to hub of one of the most dynamic regions of the country.

Much of Georgia's success in attracting new businesses and investment owes to Atlanta's preeminence as transportation, financial, and trade center of the Southeast. ''Take Atlanta away from Georgia and you could just about split up what's left between Alabama and Florida,'' one is told.

Although not in the same superstar category as Florida, Georgia has been experiencing significant, steady growth in recent years. The progress has been the result of good transportation and other infrastructure, progressive financial institutions, entrepreneurial skills among its people, and the political will for economic development.

''We are not yet caught up in the notion of not growing,'' says Gerald T. Horton, the Georgia Power Company's senior vice-president for public affairs and chairman of the Commission on State Growth Policy. ''I applaud that, because when you're poor, which we still are, if you say as a matter of public policy you're going to stop growth, you're saying that those who are poor are going to stay poor.''

Georgia employment is up nearly half a million over the past 10 years, to 2. 25 million this past June from 1.8 million or so in 1973. The state's per capita income is now around 90 percent of the national average; it was half the national figure in 1930.

The trend in nonmanufacturing employment, which covers the service industry, has been steadily up, with only a slight hiccup in the recession year of 1975, and no downturn at all through the current recession. Manufacturing employment has also increased over the past decade, though much less dramatically. Food processing employment, however, has shown a significant gain.

Georgia State University economist Donald Ratajczak predicts the next 10 years ''will be pretty smooth.''

Georgia has a well-diversified economy, with traditional strengths in lumber and pulp and paper, in agriculture, and in textiles and apparel. It has some rather specialized claims to fame as well. For example, some 80 percent of America's candy canes come from the area around Americus, in southwest Georgia. The major poultry center, Gainesville, claims distinction as the ''chicken capital of the world,'' and has a commemorative statue of a chicken to prove it.

A Georgia Power Company forecast for the state predicts that ''nonmanufacturing, service-producing industries will be the fastest-growing, with the largest gains being made in communications, finance, and business and health service. It is premature, however, to announce the demise of traditional manufacturing. . . . Georgia's shift away from manufacturing to service-producing industries will be neither rapid nor severe.''

Manufacturing companies, here as elsewhere, are surviving by automating. At the the carpet mills, for instance, machines pull soft ropes of yarn, like charmed snakes, out of the cylindrical bins in which they are coiled. And computers direct the amount of color shot onto a bolt of carpet in the dyehouses.

In the textile mills, one individual is in charge of what looks like an endless row of shuttleless looms chug-chug-chugging like locomotives ready to rip free from their platforms and roar off along the tracks.

The state as a whole came through the recession relatively well. Georgia unemployment peaked at 8.3 percent during the first quarter of this year, more than 2 percent below the national figure.

But that is not to say the recession wasn't felt, particularly in manufacturing. Though the recovery is nearly a year old, there remain in the state pockets of unemployment of 15 percent or more. Forest products and carpets got a serious jolt from the recession, although the outlook now is much improved. Textiles suffered, too, particularly at the end of the recession, says Pamela P. Brannen, assistant vice-president and economist at Citizens and Southern Georgia Corporation.

The farmers have been having serious drought problems for several years, and the recent searing heat has not helped.

''There are really two Georgias,'' says economist Ratajczak. ''There's Atlanta, and everything else.'' Then he corrects himself to suggest it's better to say three Georgias: Atlanta, the prosperous small towns, and the small towns that aren't doing too well.

Many of Georgia's small towns are bright and prosperous, although the badges of their untidy prosperity are often identical chain eateries and shopping centers.

There is still lots of local color around, though. Out on a back road one rainy Saturday this correspondent drove by a couple of senior gentlemen in rocking chairs on the front porch of a filling station-cum-general store, whose architecture suggested the '20s. Out front they had one of those electric signs on wheels, with flashing colored lights, that you rent for so much a month: ''If you can't stop, smile.'' I couldn't, but I did.

Some of the small towns seem to be assemblages of ancient wooden buildings fighting a losing battle with gravity, humidity, and Kudzu. Along the country roads one sees occasionally what look to be the cinder-block beginnings of a house, or maybe a shop, where someone started to build something but then just somehow gave up.

''But as long as the Athenses and the La Granges outnumber the other places, '' says Dr. Ratajczak, citing some of the more prosperous towns, ''we're doing all right.''

On the other hand, many small towns are one-company businesses, and poor management of that one company is bad news for the whole town. And if proximity to metro Atlanta is as important as many think, the small towns ''outstate'' are in something of a bind. Acknowledging the problem, George Berry, state commissioner of industry and trade, says, ''I think it is time that we develop an affirmative program for smaller towns,'' which are less likely to be able to attract outside companies on their own.

Meanwhile, Georgians are pleased at prosperity but unwilling to submit to a process of national homogenization. ''When people talk about 'the New South,' they mean we're becoming more like the North,'' one hears.

''But we're not going to be like them. We'll continue to be Southerners,'' says Mr. Horton.

''Legislators and governors, political leaders in the South, are really captured with trying to do two things: One is to bring the South to where it shares in the national wealth, and productivity, and so forth, and at the same time, not to lose that other South, the South of Walker Percy and Flannery O'Connor.''

Some observers, Mr. Horton among them, express concern that the people of Georgia may not be ready for the new industries. John McIntyre, president of Citizens and Southern National Bank in Atlanta, says: ''We must educate all of our people. If we can continue to push education for the lower socioeconomic groups, that's the quickest way to raise the standard of living for the whole state.''

Mr. Horton puts it more harshly: ''By every index, our educational system does not educate. Consequently we aren't producing the kind of people who can run the industries of today. What we've been selling for at least 50 years about the South is that we have a cheap labor pool. But a cheap unskilled labor pool is no longer an inducement.

''The numbers show that all things being equal, the Southern economy will become more like the rest of the country. But if that happens, the people who are here can't run that system. What may well happen is large inmigrations of people from outside.

''I'm convinced that this next 20 or 30 years is kind of the South's time. Places have their times, and this is the South's time. But it won't be uniform (across the region), so that if you fail as a public figure or a business leader to do what has to be done, particularly in the field of education, you may miss this time.''