will huge meshes always be rendered completely by the graphics-card?

Let's say I have a huge mesh, which I use as a terrain, but there is only a small portion of this mesh visible at once.
Could it be better to split up the mesh so the graphics-card would be able to render only the visible parts.
Or does the the graphics-card only render those parts of a mesh which are visible anyways?

 

a single huge mesh always runs vertex shader,
but fragment shader only runs on "visible parts".

split the mesh only if that big mesh is the bottleneck

 

Use the profiler. 9 times out of 10 problems will be due to shader choices or too much transparency and so on, if the GPU is being hammered.

I kept my response non-technical but it's the gist of things for mobile.

"big" is utterly meaningless btw. Much more interesting to know if it has a lot of verts and what shaders you're using and so on. Profile it.