hey dude, i had the same problem as you once before, but no need to fear. when you say game updates, i am assuming you are including option files and what not. I live in the united states and therefore do not have pes 6 on xbox 360. Instead, for the last yr. i have been playing winning eleven 9 international (pes 5) on xbox via backwards compatibility. in order to get updates for me, i bought this hardrive add-on called xsata. It enables you to backup files on your hardrive, memory card via your pc. It also looks really cool on the 360 (it has like a blue ring around it and it attaches to your harddrive). There are obviously so many option files all over the net for pes 5, however, i dont know what the status of the option files for pes 6 on 360 are. I am assuming you could just google it and find something, if not now, in the next few days.
You may also be ok by just purchasing the datel transfer kit, which enables you to connect a 360 memory card directly to your pc. Now that im thinking about it, this may be better for you, as you are actually playing an xbox 360 game (unlike me playing a current gen game on a next gen system). In that case, you would need to buy a memory card, and the transfer kit, then download an option file that you feel is suitable.
Good luck bro, hope this helps.
I CANT WAIT FOR PES 6 To COME OUT IN THE STATES!!!!