Depends what you mean by the DirectX redist.
If you mean the web installer linked in the FAQ - yes it will work
If you mean one of the many SDK redists then it might work... XNA needs bits from several different redists and you might not get the right combination. But this is as reliable as crossing your fingers and hoping the user has the right bits becuase they installed some other DirectX game.
There's a reason the FAQ is so clear on what you need... because thats what works. If you want to use other means to get the prerequisites on your machine then make sure you understand how they all work.
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