No difference, but why would anyone need to do this? When motorcyclists ride in separate lanes, they can both ride in the middle of the lane and thus have a full width of a lane separating them laterally. When the following distance becomes less, the motorcyclist approaching from behind can even switch their lane position so that there will be more lateral separation between the two.
Or to put it this way. Riding in a staggered formation gives a reason to have less than the full lane to yourself. Your described scenario does not. If someone still decides to do it for whatever reason, it is a separate topic, one is perfectly entitled to turning the handlebars and riding into the nearest tree if they so wish.
I don't know what exactly is taught in the police motorcycle course, we'd need to review that to actually discuss it. Riding in a staggered formation would be perfectly fine if you didn't decrease your following distance from 2s to 1s as a result, maybe except on narrow lanes where keeping to the middle would give you more space cushion to act against things like the aforementioned side wind. Besides that, the police course probably teaches several different parade formations which are not meant to be used in traffic and don't have much to do with safety on public roads.