How about international speaking engagements or when not at the official podium? I handled a head of state last year (G20 nation) and while the expected security presence was there, he used our wireless handheld, as he was in a seated interview. He did not have his own audio personnel, but a member of the embassy present to assist me did have a background in audio and we got to talk a lil shop about the 01v I was using.
As far as feedback goes, there was plllllenty of time to ring thigns out, as the security spent multiple amounts of time making sure nothing else could occur. This was in a ballroom using an overhead system. Priority was simply making sure nothing could feedback, but the bigger issue was with q&a mics for the audience. I did some generous compressing of the main guest's mic to smooth out anything out. If necessary, we could have split the input for pa and press, but it wasn't. If I needed anything, the embassy guy was there for any communication.
Not quite like handling the U.S. president, I am sure, but probably just a matter of scale. However, the U.S president does speak without the presidential podium, so what then? What would happen if he came through "my" ballroom (given that it is literally next door to the US embassy here, not the most remote possibility)?