Hi there,
Unfortunately no you would not automatically get your choice. This is really dependent both on what's available during that time and how well you performed.
In terms of the MBA, it's actually not expected! You can absolutely keep rising up the ranks without and MBA.
To maximize your chances of a successful move to another geography
1) Build a stellar reputation - do good work, work hard, and be known as "the guy/gal" for xx
2) Build your network - network agressively (yes, networking doesn't end once you've gotten the job offer). Make sure you're known by and have allies in people who make decisions such as staffing managers, Partners (specifically those responsible for recruiting/resources and who are heads of industry/function verticals), etc.
2) b). When I say network "aggressively" please don't be needy/annoying :) There's nothing worse than someone who is obviously working the room or trying to please!
3) Look out for opportunities - Look for office transfers, short-term projects, ambassadorships, etc.)
4) Practice patience and be flexible - This might take a year or two. And you need to be ready to go at the flip of a coin.