My envisioning of the style would be using a melee weapon at close distance to knock them back into bow range, then shooting the bow as a follow-up, not actually using the bow as a weapon, because as you point out, that would be quite silly. Think Raven from Tales of Vesperia:
I wouldn't want the magicks, obviously, but knowing Project Soul, they might actually implement that also, but just something along these lines.
I think that approach is feasible, but it depends on how big an emphasis you want to put on the bow; Link afterall uses a small hornbow-like bow in his (mostly Ocaraina of Time-inpsired) design for the Gamecube version of SCII. But it was a niche instrument with only a few context-sensetive moves. The greater you expand the role of the bow (in terms of both the range it is employed within and the total number of moves it is involved with) the more difficult that becomes. Unless it's some sort of spirit-energy bow, a la Azwel, there are significant pragmatic constrains in how you approach the moves and the animations if you have to be constantly pulling out or shouldering the bow. I don't know how many here have ever actually practiced archery, but a bow is a cumbersome instrument for pretty much anything other than what it was designed for, and the larger the bow the more pronounced the problems, and while Project Soul can use all of their skill and all the quick animation inattention-blindness-enabled tricks at their disposal to cover for some of that, it's still a complicated matter to make the bow work with another weapon and not be constantly clunky.
There's also the fact that drawing an actual bow takes a fair bit of time (particularly when measured at the individual frame analysis/pacing of Soulcalibur play), or else it just looks goofy; you can get away with fudging those details with a cartoonish/spritish Tales character, but it becomes much more awkward with a realistically apportioned character models that more closely approximate real human range of motion and quality of movement. I certainly think a character who uses a bow in a back-up capacity is a more realistic possibility for them to design than someone with a so-fantasy-I-can't-go-with-you-and-suspend-disbeleief-to-such-an-absurd-extent melee bow, but again, I think the larger you make the bow and the larger you make its role, the more difficult it is to work into a game like this. And ultimately, I just think it's a bad concept. Whatever a thousand hollywood movies and a bazillion action RPGs and untold legions of anime works may have suggested, bows are not meant to be a high-speed, omni-range, fit for all purposes instrument, particularly in close-quarters. They are amazing at what they do, and incredible instruments with fascinating aspects of engineering to explore, but their martial role is highly contextual, particularly when compared against the common place fantasy.
Long story short: even within the context of Soucalibur's generous take on physics, there are going to be limitations imposed by the animations and what looks just too forced. So I think a role for a bow much more expansive than that utilized by Link in SCII:GCE would be difficult to employ. Of course, you could try to make the bow a little more involved even it it weren't a core part of the moveset, to make it still a part of the character's image, even if, in practice, it's not utilized in a whole lot of animations. For example, by involving it heavily in Critical Edges, or as a finisher to combos which have already left a character stunned, allowing for the weapon mix-up and bow draw animations to be at least a little less rushed and thus absurd.
