I have never seen a Nikon F6 with a US on the serial number. The simple solution to your problem is to call NIKON USA and ask. You should get an immediate answer. I have had excellent service at The El Segundo, California branch.
As for warranty and service on gray market camera I quote Nikon USA
"Nikon Inc. USA cannot provide any technical support or warranty service on Gray Market items. Additionally Nikon Inc. USA cannot perform any fee-based repair work on Gray Market items. Please do not contact Nikon Inc. USA for help with any Gray Market products. Please contact the reseller or importer of your Gray Market items for warranty and service information as well as software updates and downloads."
My F6 also has the Nikon USA sticker inside the LCD cover. Also the serial number lacks a US prefix. I bought my F6 new from B&H in 2009. It came with a 3 year warranty good only in the US and territories. The serial number is 0032xxx.