Floating rope

For purposes of this experiment:
Our earth has a smooth terrain with no water.
We have a thin strong rope with a length longer than the earth's circumference, in this case at the equator.
Gravity is the same value along the equator.
We shall not consider any weather influences, so its a perfect sunny day, no wind.

If we tied one end of the rope to a robust pole at a metre above ground level, then proceed to unravel our rope along the equator, keeping it in tension, thus ensuring our rope is parallel to the ground; if we go around the world and return to our pole and tie the rope to it at the same height without losing our tension: Will the rope essentially 'float' a metre above ground, with its own tension and the pole holding it up.