As others have noted, the gravitational pull of other planets, notably Venus, would prevent this planet from always remaining exactly on the opposite side of the sun. I haven't done the calculations, so I'm not sure if it would deviate ENOUGH to actually be visible from our Earth.
But regardless, I suppose, for the sake of the question let's assume not. Counter-Earth is always behind the Sun or so close to the Sun that it is invisible.
Once people discovered gravity and starting figuring out orbital mechanics, they would figure out that there must be another planet of this mass and in this orbit. Neptune was discovered this was in 1846, and it's effects are much smaller and more difficult to observe than Counter-Earth's would be. So absolute latest is early 1800s. I would have said earliest is when Newton formulated theory of gravity, 1687. (I'm not sure on what basis others have said 1500s. Maybe they're making different assumptions or maybe they know something about the history of astronomy that I don't.) But I'd say that -- going by the assumption that it is never visible from Earth and we can only deduce its existence from gravitational effects -- it would have been discovered sometime in the 1700s.
As to what difference it makes to history ... hard to say. How would Earth history be different if Mars or Venus did not exist? This depends a lot on how "fragile" you think history is. Think of all those time travel stories. If someone went back in time and changed one little thing, would the effects quickly peter out, lost in the rounding errors, and history proceeds as before? Or would that one small change create larger and larger ripples until history was totally different?
In this case, if someone said, "Hey, I've proven that there is this Counter-Earth on the other side of the Sun", would people basically say, "Wow, how interesting", and go on with their lives as before? Or would it lead one person to spend a night standing on a hill staring at the sky, and while he's standing there he catches cold and dies, and he was the person who would have made some crucial scientific discovery, and so, etc. Or, would someone wonder how life on Counter-Earth might be the same or different from life on Earth, and this leads him to philosophize about why history happens the way it does, and he proposes some ground-breaking new theory that changes how we look at the world, etc.
You say this world is lifeless, so there would be no issue of people communicating with the (non-existent) inhabitants. So aside from the philosophical implications, and possible "butterfly effect" sort of incidental implications, there would be no direct effect until space travel was developed to the point where people could travel there.