No, and the two get mixed up constantly. A lot of people say they want to cross the Antarctic Circle when what they actually mean is that they want to go to Antarctica. Crossing the Circle is a specific thing that costs you transit days, because the ship has to push considerably further south. That changes the shape of the trip and what you spend those days doing.
Worth being honest about the trade. The days spent sailing south to the Circle are days not spent landing. If the line on the chart matters to you emotionally, that's a completely legitimate reason to spend them. If what you actually want is wildlife and ice, those same days buy you more of both further north.
Combining the Circle with South Georgia is close to impossible in practice. There are only a handful of such trips a season, they're expensive, and they're long, because the Circle sits on the far west side and South Georgia is in the other direction.
Before we quote anything, we'll check which of the two you actually mean.