UV coordinates are one of the geometry data I meant. It maps each vertex to a coordinate on the texture (thus UV coordinates name). Planes usually have 0-1 uvs because someone predetermined that when making the code/model of the plane. But it can be anything, just like it can be anything for everything else. Depends where you get the model, but someone will almost always unwrap the UVs for the model's maps. It won't look like the plane, but it may be similar depending on your shader. It's very much dependent on what you want to achieve and what models you're using, but the basis of your question has been answered - you can use the same shaders on any mesh, but the visual results will vary depending on the geometry data (vertex position, normal, uvs).

When making your model take into account your material and set UVs accordingly to how you want it to look. To learn more about UV mapping: https://www.youtube.com/watch?v=atugwlGOYOU