Using Pool as heat sink/source for house A/C
I have not run the numbers because there are too many assumptions to make for calculations. However, ground coupled heat exchanger and geothermal systems need a heat/cooling source/sink that dissipates the energy to maintain a suitable steady temperature range in the heat sink (pool in this case). Without dissipation of transferred energy, the heat sink/source will gradually get hotter in summer and cooler in winter until the HVAC system no longer can do the job and the pool probably will not be usable.
Remember the heat pump system pumps heat from the house and rejects it to the heat sink( atmosphere or swimming pool) in summer. In winter it would pump heat from the pool to send heat to the house. IMHO, There will be minimal heat rejected to the atmosphere in summer and very little heat absorbed into the pool in winter. That is why the geothermal systems have a lot of pipes or underground water tables to interact with and maintain a usable temperature range
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