Not necessarily. The form the OP posted is fine for most recursive calls and won't consume large amounts of memory unless the iterative equivalent would as well if you put it in tail call form:

  function f(n,acc) {
    if(n == 0) return acc;
    else return f(n-1,acc*n);
  }
  function fact(n) {
    return f(n,acc);
  }

That's exactly the structure the OP suggested and in this case won't use O(d) space if tail-call elimination is available in the language. Now, if the accumulator is growing a list result like map or some tree traversal, sure. It'll use O(d) memory. But so will the iterative equivalent.