Some games are regional while others will let you play anyone worldwide- it's all dependent on what the developers/ publishers want to do.
The servers you connect to (most times) are dependent on what region your version of the game is for. In other words, to connect to UK players you would need the UK version of the game.
I can't tell you for sure if GH III allows global play (Activision's support knowledge base doesn't cover it and the instruction manual is useless) but considering the potential lag issue and the differing release times for downloadable song packs, I'm guessing not.