It’s not the results that make models valid/invalid. It’s how well the model approximates the underlying processes that lead to the results, which make it valid.
A clock that is stuck is a poor model of time because it does not model the progression of time, even though it is still correct twice a day.
We can make a very simplistic climate model that would be valid. We have a sphere of radius 6,357km, which is illuminated by electro-magnetic radiation centered at wavelengths of 0.6um. When the light hits the surface, it is absorbed and is re-emitted as black body radiation with a wavelength centered at 10um. It has an atmosphere, which contains a gas, which blocks the escape of wavelengths at 4um and 15um. This reflects some of the black body radiation back to the sphere, causing it to warm. In 2009 for the earth, this lead to a net accumulation of 0.6 W/m^2 of energy absorption [1]. If accumulated over the entire area of the sphere and accumulated over time, this would lead to an increase in temperature. Although the model does not take into account land formations, ocean currents, air currents, seasons, etc, it still models the underlying process of the earth’s energy balance and can answer the question of whether the planet will warm and can provide estimates at how quickly this will occur.
I think you’re hinting at systems being so complex that they can vary based on minute changes in initial conditions, you’d be correct to say that climate is chaotic. Not all chaotic systems are the same though. A double pendulum will swing in eccentric motions, but if you look at something like the stock market, there’s a lot of short term variability with long term certainty. I cannot tell you what my stocks will do next week. But markets generally converge on a doubling of money in 10 years. In fact that’s reliable enough that I’m willing to have a 401k. With the pendulum, I can tell you with a lot of certainty that if it’s damped, it will settle to its lowest energy state and stay there permanently.
A climate model will not predict the weather. But in the same way that I can tell you that winter will be cold, I can also tell you that Arctic amplification and Hadley cell expansion will lead to very different weather patterns that civilization has not seen before, such as much more extreme swings in temperature and weather.
[1] https://en.m.wikipedia.org/wiki/Earth's_energy_budget#/media...