No, you can't unlock any costume for the story mode. But it could have been much worse:
All dismemberment, beheading, etc. Everything was cut probably prior to the release of the demo, as these screens seem to come from a near complete version:
It's mostly featured in the complete edition / X. I don't think the added content is worth it, they could have handled it much better.
As a reminder, from what I remember this game wasn't developed internally but outsourced. The idea behind it is good, but the execution is rather poor. And sadly the battle mode is horrible.
edit: Oh, and they changed Steve's hairstyle in the complete / X versions, to avoid him looking like a well known actor: