As long as the water level is higher in the pool than the water table level there will be no damage to any kind of pool. If the water table is higher than the water in the pool there will be damage to any kind of pool. However, the kinds of damage that you will see will vary depending on the kind of pool. A concrete/plaster pool will handle small water table differences, but any significant difference will cause dramatic amounts of damage that are difficult to repair. A fiberglass pool will initially deform a little, generally causing no damage, but then it will float out, just as a concrete pool would, and tear out the plumbing. Fiberglass will float a little sooner than concrete, but the difference is small. Fiberglass will cost less than concrete to repair, though it will still cost quite a bit. A vinyl liner pool will see the liner separate from the walls. For small water table differences that is not so serious, perhaps leaving some liner wrinkles, but larger differences will typically ruin the liner. Losing a liner is a lot less expensive than having a pool float and tear out the plumbing, but it is still damage.
Keeping the pool full of water will prevent problems. If you do need to lower the water level there are things you can do to avoid damage, for example a hydrostatic valve or dry well(s) with sump pump(s).
