I think it will depend on the resources of the embassy you go to, but I have heard of this being done through embassies overseas. Here is a link describing the process for VA Comp and Pension Exams, which leads me to believe this can be done:
The Claims Process for Veterans Living in Foreign Countries Explained
I don't think that your status in the foreign nation could/would impact how the US Embassy treats you. Plus, this is not an immigration type matter, it is a government services section matter.
Best of luck!