That's not true. You could have an arbitrary number of years that were colder in a row, with rising CO2 levels, and still have a world where CO2 causes a temperature rise. It would simply require a countervailing force that's stronger.
The noise level is irrelevant; I'm not sure why you would bring it up. If there are naturally forces that fluctuate up and down in a random walk, and CO2 is a much smaller but consistently up force, inevitably we'll wind up with increasing temperatures over time. You could argue there are larger climatic signals (not noise) that we should be concerned about, but what you actually said is simply wrong.
The noise level is irrelevant; I'm not sure why you would bring it up. If there are naturally forces that fluctuate up and down in a random walk, and CO2 is a much smaller but consistently up force, inevitably we'll wind up with increasing temperatures over time. You could argue there are larger climatic signals (not noise) that we should be concerned about, but what you actually said is simply wrong.