Some questions are bad questions. This is one of them. We can get a clearer and more useful answer if we change the question. We can avoid wasting a lot of time arguing at cross purposes.
Here's a better question: "If we used fiscal policy instead of monetary policy to remove a shortage of aggregate demand, would that switch from one policy to another have distributional consequences?" The answer is almost certainly yes, though what those distributional consequences are will depend on the exact nature of the fiscal policy.
Here's an even better question: "If we assume that monetary policy always responds to changes in fiscal policy to keep aggregate demand at the same level, will changes in fiscal policy have distributional consequences?" Now the answer is certainly yes, though what those distributional consequences are will depend on the exact nature of the fiscal policy.
[Update: now I think about it, I think my third question is actually the same as my second question; just a clearer way of saying it.]