No, if it's just getting a material without a texture, then you don't have to UV.
You're using the word surface, which I think in maya you mean material. A texture can be procedural or a file texture applied to the material, in the latter case you need to UV map the mesh as Jay says.
If you open the hypershade, you will see all the materials in your scene, and you should be able to apply the end material to the whole object.

Edit: All meshes have UVs by default, but the default ones on anything more complex than a primitive are garbage, which is why you have to UV map it yourself.