As the linked reference indicates, the ACW is a complex phenomenon with input from different ocean basins and atmospheric conditions, but which is dominated by subtropical input from the South Pacific associated with the ENSO. As large ENSO events (El Ninos/La Ninas) happen on a 15 to 20 year cycle, it is reasonable to believe that some mode of the ACW would have a period on this time-scale, which would affect the SSTA and PrWat in the Southern Ocean, which would in-turn affect a change in the Antarctic Sea Ice extent. However, I am not familiar with any particular phase relationship at the moment, but the 1997-98 Super El Nino was about 17 years ago so possibly there could be a natural mode period involved.
Peterson, R. G., and W. B. White (1998), Slow oceanic teleconnections linking the Antarctic Circumpolar Wave with the tropical El Niño-Southern Oscillation, J. Geophys. Res., 103(C11), 24573–24583, doi:10.1029/98JC01947.
http://onlinelibrary.wiley.com/doi/10.1029/98JC01947/abstractAbstract: "A case study for the period 1982–1994 shows that a major source for the Antarctic Circumpolar Wave is in the western subtropical South Pacific, where interannual anomalies in sea surface temperature (SST) and precipitable water (PrWat) form. Once established, these interannual anomalies, in tandem with anomalies in sea level pressure (SLP), move south toward the Southern Ocean. The system then migrates east around the globe through a combination of oceanic advection with the Antarctic Circumpolar Current and ocean-atmosphere coupling. The coincidence of interannual anomalies in SST, SLP, and PrWat indicates the extratropical ocean and atmosphere are tightly linked on these timescales. Large portions of the interannual SST anomalies branch advectively northward into the South Atlantic and Indian Oceans, ultimately reaching the tropics in each basin some 6–8 years after appearing in the low-latitude Pacific. This constitutes a slow, oceanic teleconnection that is unique in climate dynamics, made possible by the continuity of Earth's oceans via the Southern Ocean. In the tropical Indian Ocean these interannual anomalies move east and arrive at the Indo-Pacific transition in advance of the trans-Pacific propagation of the respective El Niño-Southern Oscillation (ENSO) phases. The interannual SST and PrWat anomalies that appear in the subtropical South Pacific are directly linked with the ENSO cycle on the equator through anomalous vertical convection and a regional overturning cell in the troposphere, the same cell that initiates fast planetary waves in the atmosphere that carry ENSO signals around the southern hemisphere on much shorter timescales."