Unfortunately, you can only "pump" water a few inches this way, at best. Yes, warmer water will rise to the top of a column of water. But in a pipe open at both ends, once the overpressure created by the water above the source exceeds the total pressure at the source (~ 1 atm.), water will stop rising. When you do the math, even very cold water at the source vs. nearly boiling water at the top of the pipe will only allow the water to rise a few inches.

(If your source pipe was insulated and could extend to great depth, and you could heat ALL of the water in the pipe, you could do somewhat better, but heating water at the inlet of the pipe would be costly and difficult enough to outweigh any benefit.)

The other error here is the usual one with solar & wind power. Yes, the energy itself can be regarded as "free," but you need land upon which to place the collectors, and even more important, you need to BUILD the collectors, and that costs money (capital investment). Even solar troughs are not free, nor are long pipes, especially (as others have mentioned), pipes that will not corrode in hot seawater. And once the facilities are built, they will need MAINTENANCE -- they will get dusty, they will corrode, microbes & insects & birds & animals will do various things to reduce their efficiency, etc., etc.

There are some viable concepts in ocean-thermal and solar-powered water pumping and desalination, but this is not one of them.