Hubble captures new image of two colliding galaxies
astronomy.com
astronomy.com
> (...) about 350 million light-years from Earth.
So, they are already together, the problem is that light is just _too_ slow so we cannot see it yet. :)
Ok, so I'm only kind of serious. In the scheme of things all things change. I expect time is limited to less than a megayear for the systems on the edges of the arms like ours is on the Milky Way.
And like you said, the distance between the stars is what prevents this from being a total catastrophe.