In theory yes, in reality, who knows... maybe?! Physically the control scheme should work fine between the two, but it may be locked out at the firmware level.
Some US bikes have EVAP/SAI, some don't. It's 50 state vs 49 state legal, CA being the outlier.
On some models, the bike will not work with miss-matched maps, no idea on the R3 if that's the case.
For example, the Roadster had zero changes to hardware from early 2012 to late 2012 and later, but you cannot use a late 2012 tune in an early 2012 or earlier bike. Triumph don't document this publicly very well, only way to find out is try and if it doesn't work, revert to the working map.
My Daytona 955i won't start with a miss-matched SAI tune in a non-SAI bike (doesn't matter if you remove it, only matters if it had the system from factory).
You can simply copy all the tables from the US tune file into the EU tune file and load that and it will work just fine.