This is pretty much 100% incorrect. The ring structure of atolls is not composed of soil or sand washed into the sea from a mountain, it is coral. Which is one reason why most atolls don’t have solid rings enclosing lagoons, they have irregular, often open, rings of islets. If the atoll were simply overwash from an island, how would the interior disappear and leave an outer ring behind? Wouldn’t the ring prevent the inside from washing away? Where would the contents of the island go if they were surrounded by a ring?
There are multiple types of sand on beaches - silica sand and coralline sand.
Sand comes from many locations and environments, and may be derived from either rock or biotic sources. It can have a source as close as rockfalls from seacliffs, or be transported hundreds to thousands of miles by streams and rivers. A portion is even carried as dust and sand in the air. Once the sand is has been washed into the ocean longshore drift moves and collects it in locations - prompting dune formation. The majority of the sand you’ll see in temperate regions is composed of silica-based rocks. Silica, what both quartz and glass are made of, is very resistant to erosion. It lasts after other minerals have been broken down and altered. In tropical regions another mineral can also be found in sand - calcium carbonate, or CaCO3
Low-lying atolls weren’t all formed by rain wearing down volcanic rocks.There may be some silicate sand, but it’s not the primary method of formation. Any underwater feature within about 30 meters of the surface will tend to grow coral in the tropics, unless the physical conditions work against it (extreme current, etc) Once coral forms a barrier to currents, then sand deposits start. Largely aided by the creation of new calcareous sand by the mechanism of sea life grazing on coral and by mechanical action breaking up pieces of coral.
Technically, any island which has an above-water rocky component is not an atoll, but an island with a barrier reef.
In the Eastern Pacific, tectonic plate movement is causing island subsidence, not sea level rise. The islands do erode a bit, but the significant vertical change is from tectonic subsidence. The oceanic plate is sliding under the continental plate of North America. The volcanoes are getting lower, not the sea getting higher.
Saltwater doesn’t “intrude” on a Ghyben-Herzberg Lens in the way most people think, but human activities can often interfere with the mechanism of lens formation and replenishment. If your well siphons up from the bottom that is now below the freshwater layer, is that really “intrusion” into your drinking water?
Atolls don’t just “wash away”. It is possible for an atoll to drown if the water depth gets to be too much for coral to continue growing at the rate the island is sinking, but normally, the coral just keeps growing as long as it is above 30 meters. The shape of the atoll would probably change in relation to the bottom contours as the growth zone gets wider or narrower, but the atoll doesn’t just “wash away”.