the Botany Bay was launched in 1996, and since Nero alters the timeline in the 23rd century, then presumably yes, its still drifting in space....
The general rule of thumb seems to be that which took place before Nero's intervention is the same, everything after is either altered or will no longer take place
I'll show myself out....
What is the likelihood that they are going to show the Botany Bay on the big screen looking exactly like it did in "Space Seed"? Or that Khan's backstory will be tied to 1990's Eugenics Wars?
The temptation, and probable need, to contemporize those details is going to mess with a single point of diverence theory.