Yes—the camera will fire as soon as the active AF point sees something in focus at the preset distance. Turning away is just a way to avoid an immediate shot while you press and hold the shutter.

The key is that after pre-focusing, you do not refocus again with AF-ON. You hold the shutter down and wait for the subject to enter the plane of focus under the selected focus point.

So if you point the AF point directly back at the branch you used for pre-focus, it may fire immediately on the branch. In practice, you’d compose so the focus point is aimed where the subject will appear, not necessarily on obvious clutter that is already in focus. In a busy scene, branches or background at similar distances can indeed trigger the shot early, which is a limitation of trap focus.

For your bird example, trap focus works best when the landing spot is predictable and the AF point can be placed where the bird will enter focus without another object triggering it first.