Yes there are persisted data structures and databases built on top of them. The whole type system applies to persisted data structures so you can make your own data structures and fill out a few type class instances to query them with plain list comprehensions (e.g. btree indexes are defined and queried this way in some internal tools).

Eager Haskell with a structural type system, deterministic garbage collection, and no overloading penalty, that would be a fair summary.

It'd be interesting to see how GHC would do in the same area, there would be some significant challenges. I haven't tried to use GHC there so I can't say.