Yes, you can change the relationship of the shift mechanism to the mount flange so that you can apply shift vertically when shooting in the portrait orientation. This is pretty much a design feature with most tilt/shift lenses designed for use on SLR type cameras. Where your lens, along with the TS-E 17mm f/4 L, expands the capability of other T/S lenses is that the relationship between the shift movement and tilt movement may also be altered in varying amounts between 0º and 90º on the fly.
This review at The Digital Picture details the various movements available with this lens. Scroll down about halfway to the point where there is a sentence in bold type that says, "The TS-E Dance." The rest of the review shows the effect of the various movements this lens is capable of.
From the above referenced review:
Like all of the TS-E lenses before it, the entire lens rotates on the lens mount to allow the tilt and shift features to be oriented as desired. The lens rotation will lock at -90, 0 and 90 degrees (180 degree total rotation) and will click (semi-lock) every 30 degrees. The small tab near the lens mount that unlocks the lens rotation is easy to access when holding the camera grip.
Also from the above referenced review:
Like no tilt-shift lens before it, the TS-E 24 L II's tilt feature rotates independently of and in relation to the shift movement. This is a really nice feature - its called TS rotation. In the past, the orientation of the shift and tilt mechanisms could be changed in relation to each other, but it meant taking the lens apart with a screwdriver (or sending it to Canon Service if you were less adventurous). And even then, the movement orientation options available were either perpendicular (right angle) or parallel to each other (2 options). Now, rotation of the tilt and shift features can happen independently of each other. The tilt-shift relationship can be changed by varying amounts up to 90 degrees on the fly. TS rotation locks at the parallel or perpendicular settings relative to the shift orientation and clicks at 45 degrees. You can use non-click settings for either rotation mechanism on this lens, but care must be taken to maintain that setting (no lock is provided for the 'tweener positions). The small tab near the shift locking knob (closest to the lens mount) unlocks the TS rotation.