Layer Memoization and KeyValueStore Provisioning

Question on layer memoization, given:

SomeLayer.pipe(
    Layer.provide(KeyValueStore.layerFileSystem("./_cache")))

SomeLayer.pipe(
    Layer.provide(KeyValueStore.layerFileSystem("./_cache")))

SomeOtherLayer.pipe(
    Layer.provide(KeyValueStore.layerMemory()))

SomeOtherLayer.pipe(
    Layer.provide(KeyValueStore.layerMemory()))

Will both layers actually get the file system kv store?

Layer Memoization and KeyValueStore Provisioning - Effect Community