Depends on how the game set's it up and it's "gaming server". Some games let's you choose your region with the best connection. Some matchmake you with the best available server. eg Call Of Duty 4 doesnt let you choose your region, just (matchmake) connect you to whatever's available be it EU, US, OZ etc etc. Whilst other games have a better lobby system where you can choose which server you want to connect to.
I get alot of my games form HK as well as it's much cheaper over there. You shouldn't have any problems. You should still check forums etc regarding this matter but the only problem I can see is downloading content as some of it might region based. Like the map pack for COD4 which had compatability issues with the map patch bought from OZ but the game was purchased from the US. Didnt work.
Hope this makes sense.