Geoff,
Look at it this way.
An exact duplicate of the universe in 1906 is created and runs parallel with the current universe with no external intervention in either.
You have just introduced the modal definition of "necessary". Something necessary would have to be the same both duplicates whatever happens. Something which is necessary is "the same in all possible worlds".
So now we have four notions of necessity? This is why I didn't want to discuss modal logic, and why I am losing the desire to continue responding to the technical debate about the exact relationships between these different senses of necessity, possibility and contingency. There are different forms of modal logic which define different relationships between them.
Will both universes be identical in 2006?
If hard determinism is true, then yes.
If it isn't, then possibly not.
Whether it is or it isn't, some things will always be the same, and these are necessay. Anything which is possible of not being the same is contingent.
Or is it possible, say, that a person might exist in one universe and not in the other?
The following use "possible worlds" definition of necessity and contingency:
Question: "Is the Prime Minister of England necessarily Tony Blair?"
Answer: "Yes, Tony Blair is necessarily Tony Blair". ("De Dicto" reading of the question)
Answer: "No, Tony Blair might have lost the last election." ("De Re" reading of the question)
Even the first answer can be challenged. What if in one possible world, the fertilised egg which became Tony Blair in this world split and T.B. was a twin? Which twin is Tony Blair? Answer: Neither. Tony Blair couldn't have been a twin. It gets worse. What it one of the embryos died before birth, and the one which survived became Tony Blair (this could have actually happened)? Did the twin go back to being T.B. when his unborn brother died?
Messy, messy.....
The above post is taking us into the area of philosophy known as "essentialism", which is exactly where it was always destined to end up once we started analysing the notion of necessary beings and contingent universes.