First... No need to be such an Alarmist -
Yes the Galaxy 3 has an ODIN counter and a Modification Check which will change to show modified when a Custom Rom has been installed...
Yes it is possible that upon returning or submitting your phone for repairs the person might check your odin count...
with that being said...
ODIN is used to flash factory firmware on an uprooted phone or ROMs, Kernels and Modems on a Rooted phone... SO - if you did not root your phone and used ODIN to flash factory signed tars then there will be no increase in Odin count and download mode will not show MODIFIED.
IF you are rooted, then your phone is already warranty-less so the increase in ODIN count is not going to matter..
Second.... Triangle Away has nothing to do with the Processor... and everything to do with the firmware - The app works on the GSIII and resets odin counter but will not remove modified label. However if you are returning your phone for repair you will have to revert to stock firmware and this will automatically remove the modified tag as also mentioned in
Chainfire's thread.
Finally... The USB jig has worked on every galaxy since the first. On the epic touch there was a small modification to the kernel to support the ICS firmware. There is no foreseeable reason why the jig wont work on the US version of the SIII.
With all that being said... its good to be aware of what pinoymutt said... but don't panic and educate yourself before using anything from XDA