The takeoff config warning does not (so if you did try to takeoff with one engine but with everything else set properly, you'd get no warning), but the takeoff config advisory message you're required to check for on the before takeoff check does. You will not see that message unless you have both engines running.

So checking for the second engine running is redundant and not really necessary, but in the end it's a pretty quick and harmless way to make doubly sure things are the way they need to be. Not a big deal.