More efficient DFS on trees
If you want to cover the entire tree then your algorithm must run in $\Omega(n)$, assuming $n$ is the number of nodes in the tree. You are right, however, that you could optimize the code by checking that the child is non-empty before calling the function. This is an optimization that the compiler probably wouldn't do on its own. This optimization could improve your algorithm, but its running time will still be asymptotically $O(n)$ (assuming $O(1)$ processing per node); at most you improve the constant.