While it is true that the long term integral (climate) of a chaotic system (weather) is not necessarily chaotic, that does not apply very well to model driven climate predictions (and models are where almost all the AGW noise comes from).
The models use finite element simulation of atmospheric physics (and sometimes of other phenomena), cycled over and over again through time. This is exactly the same process used by the weather forecast models, and at least in one case (that I know of), the same model is used.
Meteorologists know that specific forecasts from models are rarely worth looking at more than 5 days out, and weather models are basically worthless for anything at 15 days out. The reasons include chaos, lack of resolution (requiring parameterization to account for the inability to simulate in detail), and lack of good initialization data. The same problems apply to climate models, and in addition, the climate models are very hard to calibrate due to the poor quality of paleo-climatic data.
So while chaotic weather doesn’t imply chaotic climate, modeling techniques, subject to chaos and used for both, produce chaos in both.
