The key is that the further into the future they look, the more uncertain the results of modeling chaotic system become, whether you average them or not. All averaging does is abstract away the underlying behavior, and in the absence of any additional information (variance for instance) is essentially useless for drawing conclusions from the model.
The previous poster is correct: chaos limits your ability to predict the exact state of the system (e.g., the weather over Sydney in 2093), but it doesn't necessarily limit your ability to predict statistical averages (such as the global surface temperature). Certainly there is wide uncertainty in predicting global average quantities, but this is generally not related to chaos. It's more a function of model structural errors and input parameter uncertainties.
Now I'm sure climate scientists are publishing a little more complete statistical analysis of the results of their modeling experiments. However, when they communicate their findings to policy makers and the general public, they seem to have some difficulty expressing the full scope of such an analysis, and instead point to the average or possibly a most likely outcome without the benefit of the additional information which is necessary to properly contextualize the single number.
A full uncertainty analysis of climate models has been difficult because of their complexity. (You see the same problems in many other fields that rely on large computer models.) But there are statistical uncertainty analyses of climate models, and the IPCC has been continually adding more discussion of uncertainties, error bars, etc. to its reports including summaries for policymakers.
The only way to validate them is to continue to tune them against the historical record.
Climate models are generally not tuned to the historical record, in the sense of fitting them to a historical temperature time series or something. They are tuned to data, however. This is a bit subtle, so let me elaborate:
Typically, climate modelers don't try to tune the entire model at once. They isolate subcomponents of the model, such as the cloud parameterization, and tune that. And they usually don't tune it to time series data or trends. Rather, they try to tune the submodel to the mean climate state over some period of time (e.g., to reproduce the average cloud cover in the 1990s).
This does have potential for overfitting, but by tuning subcomponents individually, they reduce the potential for compensating errors between components, and by tuning to base climate instead of climate trends, they try to keep the tuning independent of the human changes or "forcings" which occur over longer periods of time. It also allows for "independent" validation on later periods of time beyond the period of baseline climatology.
In addition, climate models can be "validated" against completely different periods of time that were not used in any tuning exercise, such as to reproduce the climate of the Last Glacial Maximum, although this is only approximately a validation due to data and input uncertainties.
In short, no, you can't truly validate a climate model's predictions for the next century without just waiting a century. (You also can't avoid tuning the model, which will always have unknown effective parameters that can't be calculated from first principles.) But you can build some confidence in the model physics through weak tuning, separation of concerns, and testing of subcomponents on independent data.