In fact, the opposite is true: it is skepticism of global warming that depends on the correctness of GCMs.
In the simplest model, which any kid can test in middle school, you take a plexiglass box full of air (representing the atmosphere), add some extra CO2 to it, and see if the temperature goes up. It does.
Well, since the mid-1800s, we have been adding CO2 to the atmosphere. We know that we've burned a lot of fossil fuels (that were underground), and we have directly measured an increase in the amount of CO2 in the atmosphere. So based on the simplest model, we'd expect to see the temperature going up. And we do! Yay, science works.
Of course there are a lot of ways to say that the simple model is wrong. But they all involve the construction of a more complex model. In order to see if anything will mitigate or compensate the basic physics of how more CO2 traps more heat, you have to add in additional factors.
So when someone goes on and on and on about the shortcomings of super-complex GCMs, remember this. GCMs are important tools for making detailed predictions and policy decisions, but we don't need them to predict the basic fact of global warming.
In fact the original hypothesis of global warming dates back to about 1900, well before anyone was using computers to model anything. The theory of global warming rests on basic thermodynamics, and it was first proposed not long after those basics were discovered.