Factor in the information from the question "Does causation imply correlation?", "Mathematical Definition of Causality", and "How to formally tell is one time series affects another".
Let $y = f(x)$, where $f$ is continuous and differentiable. Does this guarantee that $x$ will Granger-cause $y$?
Given that $f$ can be horribly nonlinear, it seems that there are a limited number of tests and methods for conditioning the data in such a way that the granger causality test can be applied effectively. Even something like $y=e^x + \epsilon$, where $\epsilon$ is white noise, can cause problems with estimating the order of integration (thus testing for cointegration, and then Granger-causality according to the Toda and Yamamoto method as described in Dave Giles' blog post).