Is it allowed to use an ex-military aircraft overseas?
If it has an N-number and an airworthiness certificate that allows the operations you want to perform with the aircraft, it doesn't matter what it did in a past life, you can operate wherever the country that controls the airspace will allow you to do so. As was mentioned before, the regulations of the country in which you wish to operate the aircraft are more relevant to what you want to do.

If on other other hand you have an ex-military aircraft that has an N-number but an exhibition-only experimental airworthiness certificate for a warbird, to pick an example, or some other type of restricted certificate, you're likely to be required to notify the FAA where and when you intend to fly it, and that may trigger additional oversight and possibly a denial of the permission to do so in a foreign country. The operating limitations document of the airworthiness certificate may also limit you to specific airspace within the US. Check the aircraft documentation and see if the FAA already put limits on the helo's operations.

That's where you will find the answer from the FAA point of view.