This is as good a place as any to put the random revelations we have about the post-SC2 continuity in the SC2 finale.
For the Mark II itself, I always figured it was the same ship the Slylandro referenced.
"..Sullen Plummet remembers that the last time the Shaggy Ones visited our world they came aboard a great circular starship, one even larger than your own. They had discovered their Answer and were leaving to go somewhere and they didn't tell us exactly where `somewhere' was."
So finding it is probably even more significant than just fidning another random Precursor vessel.