Assassin's Creed: Brotherhood, it's possible to leave the Animus and explore Monteriggioni as Desmond Miles in the game's present-day, 2012. However, users on the game's forum are complaining about a nasty glitch where they're unable to sit back down in the Animus after running around the Auditore compound, effectively trapping them in 2012 and halting all progress in the game. You can see the glitch for yourself in this video, though the resolution is fairly low.
We've contacted Ubisoft to see if there's a workaround or patch in the works. We'll update the post as soon as we hear back.