The confusion here is caused by the way so many people incorrectly describe what the "shift" function actually does. Shifting the lens does not alter the scene perspective at all, it simply causes the image sensor to be moved to a different part of the image circle being produced by the lens.
For example, the Canon TS-E 24mm f/3.5L Mark II creates an image circle which is so large that it actually represents the same view that would hit the image sensor if you were using a 17mm lens (to the best of my recollection; possibly it's a 16mm). But when using the TS-E lens only a small part of the image circle is hitting the camera sensor (or 35mm film frame if you're old school). Shifting the lens up effectively causes the image sensor to be moved to the part of the image circle which represents the scene further from the ground (the top of the building, for example). Shifting the lens to the left effectively causes the image sensor to be moved to the part of the image circle which represents the scene to the left of centre.
In other words, shifting a TS-E 24mm lens is exactly the same as capturing the same scene with a standard 17mm lens, and then (in post-processing) drawing a selection marker (with 3:2 aspect ratio and a width and height being 70% of the full size) and moving that marker around the scene (up/down/left/right, or diagonal) until it contains just the relevant part of the scene (the top of the building, without the road/pavement, for example) and then selecting "crop to selection". Shifting the lens does not alter the perspective of the scene at all, just which part of the scene you actually capture on the image sensor/film. The benefit of a lens "shift" is that it does this scene cropping without losing any of the resolution of your sensor/film, while the post-processing software crop will leave you with only 49% (0.7 × 0.7) of the megapixels your sensor can capture.
This moving of the image sensor around the image circle is what allows you to take multiple shots by shifting up/down/etc to capture more pieces of the scene, and then stitch the pieces together to create a view which is closer to the angle you'd get from a 17mm, but with higher resolution than you'd capture with a standard 17mm (because you're adding pieces together).
As scottbb mentions in the comments, shifting the lens does slightly alter the view of the scene. This will generally cause no problem, unless you're trying to capture multiple images to stitch together, in which case the change caused by moving the lens may cause parallax errors (especially where your scene mixes close items on top of far-off items, such as stair rails, chain-link fences, glass with writing or graphics on it). To avoid this problem you need to make sure that you move the camera body (the sensor/film) instead of the lens, and there are various tripod utilities which make this possible, either by holding the lens fast, or by allowing you to shift the camera body in the opposite direction to the lens shift so that the lens ends up in the original position.
As for the plane of focus, this depends upon two things: is your camera sensor/film plane perfectly parallel with the columns in the scene, and is your lens of a high enough quality that it doesn't suffer too badly with field curvature. If your camera is parallel with and focused on the columns, then they should (in theory) now be in focus from bottom to top no matter how tall they are, and no matter in which direction you shift the lens. But no lens is perfect, and field curvature means that the large image circle may suffer from an imperfect focal plane, such that instead of being a perfectly flat plane it is slightly concave or convex. But that's somewhat out of your hands, and if you do detect this being a problem then stopping the lens down to a narrower aperture may alleviate it.
Oh, and the last thing to mention is that if you shift a lens to its limit (such as ±12mm on the Canon TS-E 24mm) then the extreme edge is likely to be rather soft. This is somewhat inevitable (because you're then capturing the very edge of an unusually large image circle) and tends to be visible well before you view the end result at 100%. This could be mistaken for the top of the column being "out of focus", even though that is not the cause. So avoid shifting to the extreme unless you simply can't capture the relevant part of the scene without doing so.