If my site was always number 14, but after todays update it is showing up as number 3 on some dc's, does that mean my site will be number three?
It's possible that the addition of a link / content boosted you up in the serps, but it might drop back down. If it is stable at #3 for a week, then I'd say it is staying there for a while
after a month and google updates its database you will move around a bit for certain words that you have anchored down through advertising.
Yes I do think seeing rankings changes on other data centers is usually a sign that those same rankings will update on other data centers in time. Of course things still can fluctuate by the time the other data centers update. I wouldn't just sit and wait to see though. I would take this as a good sign and all the more reason to keep building more and more backlinks.