I'm in Blender and working with a pre-existing 3D model- I want to add more length to it, but I don't want to mess with the mesh- Is it possible to extend the texture beyond the mesh without changing it, or will I have to change the mesh anyways? Are there any shortcuts around changing the mesh?
Textures are applied to the faces of a mesh, so textures cannot be anywhere there isn't a face for it to appear on. "Adding more length" to a mesh pretty much implies moving some of the vertices. I don't think you're going to get around that.
Now if you are assembling a game world, it's quite common to have modular mesh pieces that can be aligned end-to-end, or placed intersecting each other, to form larger structures—like a wall panel that can be duplicated several times to form a longer wall, for instance, without needing a new mesh to be built specifically for that wall.