You're going to need some sort of radius, yes. There are a few reasons:
- Zippers don't form rigid angles. The forces within the zipper teeth resist bending beyond a certain radius. Grab a pair of jeans and try bending the zipper. See how it works against you? If you try to sew a zipper around a 90-degree corner, the zipper will sort of stretch like this.
- Even if you sew a zipper around a really tight corner with a small radius, the zipper won't open and close smoothly. The slider will get caught at the corners, making for a poor user experience.
- You can sew leather as a box shape if each side is a separate panel. But remember, the seams need to go somewhere, which might ruin the rigid shape you're looking for.
So either you'll need to change the design to accommodate the zipper, or change the type of closure. I strongly recommend going to the mall one day and looking at leather bags to get some ideas. Purses, briefcases, whatever.
What's the purpose of this bag?