Sure, GE allows overhauls on their big engines outside of the US but unless US airlines are willing to send their work overseas, it isn't relevant.
again, if you can let me know what engine overhauls AA or DL send out of the US and I suppose UA now for their GE 90 engines.
specific to the OP's question, can you tell me who other than AA or GE is servicing AA's 773ER engines?
thus, my response is based on where US carriers would seek engine overhauls and specifically AA or DL's on the 773ER/772LR....
for a bonus, you can throw in Air Canada