Why do you even need a pump. If you can locate the pipe in a manner that it is higher than the pool, ( your roof),you should be able to let water from the bottom of the pool flow into the bottom level of the pipe and the natural convection of the water rising in the pipe as it heats up should supply heated water back to the top of pool. No need for anything electrical and the water will only circulate if the water in the pool is cooler than the water in the pipe. If you use a check valve to prevent flow back to the pool from the bottom of the pipe, it wouldnt even need to be a closed system.
This is called a thermosyphon system. It works IF the solar collector is BELOW the storage. Cold storage water is routed down to the bottom of the collector where the water heats, expands and rises to the top of the collector in vertically arranged interior riser pipes. The heated water then flows through a rising pipe back to the top of the storage. Both the outlet and inlet pipes, when used for a pool, must be below water line. The top of the collector must be no higher than the top of the storage for it to work well. There has to be a difference in temp for it to flow and it always tries to get the hottest water to the highest location. This is why the top of the collector must be below the storage. These kinds of systems require a large difference in temperature between the collector and the storage, in this case the collector (black pipe) and the pool. A large difference in temp means a lot of loss to the environment from the black pipe. So, by it's very design it is very inefficient because we want the collector to run as cool as possible. In your design you are giving up efficiency to save on electricity and by doing so are defeating the ability of the system to produce very much energy. It's a bad trade. A thermosyphon system requires glazed and insulated collectors.
There are two reasons why your design won't work in this case. The heat source is above the pool and the collectors are running too hot.
If the collector is placed above the storage, the water in the collector gets hot, but it cannot fall back to the storage because hot water rises. This system is sometimes called a batch system and the water from the high tank is forced down with water pressure when a faucet is turned on.
Pool heater sizing starts at about 50% of the area of the pool in collectors. Of course there are a lot of variables such as wind, pool shading, desired temp, pool cover or not, latitude, collector orientation and slope, etc
I'd like to see some pictures of your system. Can you post some?