I have that brand (bought used for $20), and it works.
The idea is that the bracket will rotate the flash back to still be directly ABOVE the lens, even in the sideways portrait orientation. That puts most of the shadow hidden directly behind the subject.
For TTL, you will likely need/want the SC-28 cord for the flash then. I use an older SC-17 cord (plentiful on Ebay), which still works fine. Or - the wireless Commander likely works fine too, even if the angles suggest it cannot.
Because your shooting position in this photo is well below the subject, it is going to be difficult to avoid the shadow even with a flash bracket. It will help, but the shadow may not go away completely.
Rotating the camera up on end sideways puts the hot shoe flash at the side of the lens, causing the bad (visible) shadow at other side of subject.
From any camera angle, if the flash is put back directly above the lens, then any shadow will be "below" the subject. Generally, this hides any shadow behind the subject, slighly below their head. If the flash is centered over the lens, there are no side shadows.
Exceptions are for items like outstretched arms (or guitar necks), when the shadow will be below them too. For standing subjects, this is generally a very limited condition. The flash bracket is a standard tool for wedding photographers shooting everyone at the reception. If used hours every week to produce income, it seems warranted to spend bigger bucks for it. If used seldomly, we can get by with much less "convenience".
Or, if you have enough pixels to crop it heavily, just do not rotate the camera up on end. Crop the picture instead.