Haskell compiles down to C- first, which is an even less expressive version of C basically, so you are right there. But if you go low enough FP concepts pop up

Haskell compiles down to C- first, which is an even less expressive version of C basically, so you are right there. But if you go low enough FP concepts pop up again, e.g. out-of-order execution is pretty functional, but to a degree so are vector instructions. And this is no surprise, Turing machines and lambda calculus (and recursive functions and anything Turing-complete) are equivalent. If you think about it, a Turing machine is just as side-effect free in itself, side effects are special to computers.