Yes but even if it were, which I wasn't saying it wasn't, that realities timeline progressed exactly the same as ours from our perspective. Imagine all the events that 40k describes are happenig now, we just aren't aware of it. There could be eldar and orks beating the living fuck out of eachother right now but we are stuck here, on this world, so we won't know it. The emperor could be walking among us, hell, he could be a member of the NFL( kidding). That's the perspective 40k takes. It could be a different verse, but that different verse, if we were to take our time and travel to it at the same point in time we are at, nothing really significant would have changed. The universe, the galaxies one, would still be about 13.7 billion years old and the earth would still be 4 bil old... But orks and eldar would be going at it.
Also, Sol is the same as we know it now, nothing about it is different. What removed the water was the wars, from what I remember. If it were something like a Sol expansion, it would have been noted. Although it is very neat to think about.
Although the timeline could be very very different, as you said, it is just that if it got hot enough to totally remove the water from Terra, or to the extent it is in 40k, it should be too hot for life. Could be wrong though.