"Stretching" over stretcher bars is simply a form of display. (It's more like "pulled tight, edges/corners folded over and stapled" on the wood frame vs. significantly stretched.) So, "No, ya don't have to stretch canvas."
FYI: For future reference...
When crafting/printing art intended for gallery wrap one needs to take into account an extra 1"-2" of canvas on each edge needed to accomodate the "stretching" (wrapping). For example for a 16" x 20" gallery wrap, the printed canvas would need to be 18" x 22" (assuming a 1" edge on each side).
Anyway, several pieces of art that I have created ended up mounted behind glass in traditional frames - some wooden, a couple metal in fact. They look great if I do say so myself.
So go for it. You're the artist. You get to decide!
Good luck on your project.