Did Sisko ever serve in security? Now that I think about it, we really don't know too much about Sisko's past. Other than his father is a chef, his mother was a prophet and his wife died at Wolf 359.
In what capacity would a diplomat and a military dude have regular contact? Does this suggest that Starfleet provides security to Federation diplomats?
That was never expressly indicated. I know of at least one of the novels indicating he was chief engineer of the Okinawa
before being promoted to first officer, with a few episodes indicating his engineering experience. Maybe early in his post-Academy career, he was a "utility player" like Lieutenant Leslie on TOS and Worf and O'Brien in the first season of TNG.
The OP's hypothesis is certainly sound, especially with inconsistencies early on about whether or not Curzon was a Starfleet officer. For instance, Sisko mentioned they "served together on the Livingston
". And when Bashir was assigned to show around a group of ambassadors, Sisko mentioned Curzon used to dump those assignments on him, and now has the privilege of doing the same to Bashir.