I wouldn't be concerned about the sun. Marble statues and buildings have been standing in the sun for centuries in Europe. However, I would be more concerned about the chlorine, salt, calcium (I think some marbles have more calcium than others) and other minerals in your pool and any acid that splashes on it. If you start out polished, expect the marble to etch and the polish to wear -- leaving you with more of a honed surface over the years. A softer marble with more calcium may pit and erode even more.

I have marble tile in my entry and on my kitchen counters. Love the counters, but never thought of putting it in a pool.

Also -- I know you said above the waterline, but anything around a pool is subject to splash and to the elements -- wind, dirt and dust, other pollutants and water create more problems than sun itself.

My other thought was that changing above the waterline seems to imply that there will be another tile at and below the waterline. We currently have a back wall with 2 different tiles plus the coping -- and we are planning on changing it. The pool came with the house -- they weren't our choices, so it's probably easier for me (than the previous owner who chose it) to say that it is choppy -- doesn't flow and looks like they tried to do something that they didn't work. That doesn't mean it can't work -- just be careful about what you put together and why.

Marble has been used with water for centuries.
That said it is a calcium carbonate so acid will eat, and etch the finish.
In general your not going to be pouring acid on it. It probably wont get wet more then marble used in showers, and bathrooms.
If you like green there are "Serpentine" marbles that are harder and are not effected by acid, actually not really a marble but usually refered to as that.

I’m thinking of doing the same. Did you use the marble?