I believe the chain is synchronized, so if one does, then they all probably do.
Not true. Some McDonalds are franchised, while others are owned outright. I remember a number of different occasions when the two McDonalds' near me, one which is about 2 blocks away and the other about 8 had different items on the menu. For example, for the longest time I was able to get a McRib sandwich (which happens to be the best thing they've ever served
)at the closer McDonalds but not the other one.
So no, I don't think its necessarily for certain that they all have the same stuff.