You're correct that the Type S die can be adjusted to provide partial neck sizing. Unlike the competition neck die which has a spring-loaded collar, the Type S will just let the bushing ride the case mouth up until the top of the bushing stops and then it will size to whatever degree is left.
The real question is whether using the unsized portion of the neck to center the cartridge in the chamber is practical. I think this is not an optimal solution for a few reasons. First, let's consider what we're really after - we want the bullet to get a good, well-centered start in the rifling. Now let's look at a few scenarios to get there.
A case that is only neck sized depends on the case body itself - or at least that's the theory - to center the bullet. In reality, the case is banana shaped to a greater or lesser degree, but always curved and it is highly unlikely that it will actually put the bullet into perfect, straight alignment in the throat. The fully resized neck and a bit of clearance in the throat mean that the bullet is likely pointed off center to some degree, following the curvature of the case.
A case that is full-length sized, but only partially neck sized, which is the condition you describe, depends on the unsized portion of the neck to center the bullet. The resized case body is still banana shaped, but has been sufficiently reduced in diameter at the shoulder to keep the curvature from wedging the case within the chamber. Now, we get to the unsized portion of the neck. There is approximately 0.001" diametrical clearance to the chamber neck on the unsized portion just from normal brass springiness. There is probably no more than 0.0005" diametrical clearance between the bullet and the throat and in many cases as little as 0.0002" clearance. In other words, there is one-half to one-fifth the clearance in the throat that there is in the unsized portion of the neck. Which is doing the alignment? If that were all, we could say there's no harm done by the partial neck sizing, but that isn't the whole story. Unless the bullet is perfectly concentric to the neck, there exists the possibility that the bullet's alignment in the throat is being influenced by the neck's eccentricity in relation to the bullet. If you're relying on two points to align the whole, those two points had better be perfectly concentric. The longer the unsized portion of the neck is, the greater likelihood of the neck inducing a misalignment in the throat due to imperfect neck to bullet concentricity.
Now the last scenario, a full-length sized case in which the neck is also fully sized. There is clearance at the neck and in the body of the case, the closest fit anywhere is the bullet in the throat. If the neck to bullet concentricity is good (although it needn't be perfect), then the bullet will find good alignment in the throat and the case body and neck will have minimal influence. Let's not forget that the base of the case is supported by the bolt face or the extractor to a certain degree as well; this is yet another influence on alignment. As you can see, there are several points from base to bullet that can have an effect. My procedure is to minimize the influence of those that I can control, namely the case body and neck, and let the alignment be dictated by the fit of the bullet in the throat and to some extent by the bolt's support of the base. Barring a seriously out of square case head, I don't think the bolt can have a negative effect on alignment, only a slightly positive effect from minimizing "case droop" in the chamber. Given that a resized case will usually have a maximum of 0.001" diametrical clearance at the web, this isn't much of a factor anyway.
In conclusion, I believe that allowing the bullet to find a relatively stress-free alignment in the throat by full length sizing (including the neck) and turning necks to enhance concentricity gives the bullet the best probability of a well-aligned start into the rifling. Additionally, I place a high value on easy bolt operation and true full length sizing helps that quite a bit. I favor easy bolt operation as a prone shooter because I keep the rifle in my shoulder for the entire string and struggling with the bolt not only can shift the buttplate (always with adverse consequences) but it is also a distraction from my attention to mirage and wind flags which ideally occupies all of the non-aiming time.