Yes, as long as you require() the ModuleScript from a server script.
A ModuleScript cannot run without another script calling require() on it. Once it happens, it runs on the same peer it was required from.
So if you require it from a LocalScript, it will act like a localscript, meaning you can access LocalPlayer, FireServer(), etc.
However if you require it from a server script, it will act like a server script, meaning you can use OnServerEvent event and replicate stuff to all clients.
(Note when I say "act like a __ script", I don't mean stuff such as lack of Disabled property in ModuleScripts)
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I don't currently have access to roblox studio, therefor I can't test it out.