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From my understanding, the objects would get clipped. Is this correct? And how would this affect performance? Does OpenGL ES then just stop processing the polygons which are in front of the near plane or behind the far plane?
Your understanding is correct, these are clipped away. But keep in mind that this clipping happens after the vertex processing stage (transform and lighting in ES1, vertex shader in ES2). So only the rasterization and fragment stages (texturing in ES1, fragment shader in ES2) profit from this. The vertex stage always processes all polygons you send to the GL for drawing, as only after that you know their coordinates inside (or outside) the viewing volume (normalized device coordinates).