You are confusing dynamic typing vs static typing with run-time execution vs compile-time execution.
A statically typed language can do arbitrary stuff at run-time too that will not be amenable to static analysis. This has nothing to do with the type system.
Furthermore, a dynamic language can be perfectly amenable to static analysis. For instance, in lisp+slime, slime-who-calls can identify callers of a particular function, even when grep would not, e.g. if the function was invoked via a turing-complete macro. The key thing here is that the AST to be analyzed does exist at compile-time; it just happens to be generated rather than hand-coded.
A statically typed language can do arbitrary stuff at run-time too that will not be amenable to static analysis. This has nothing to do with the type system.
Furthermore, a dynamic language can be perfectly amenable to static analysis. For instance, in lisp+slime, slime-who-calls can identify callers of a particular function, even when grep would not, e.g. if the function was invoked via a turing-complete macro. The key thing here is that the AST to be analyzed does exist at compile-time; it just happens to be generated rather than hand-coded.