This sounds like a total minefield. You might get a response in the same format, but I imagine it'd be very easy to break an API user who accidentally depends on performance characteristics (for example).
AWS RDS and Aurora both support synchronous and asynchronous lambda invocations from the database. Should be used very carefully, but when you want/need a fully event-driven architecture, it's wonderful.
Postgres can run arbitrary code too, but at this point it just makes more sense to create a service that acts as a database and translates sql to whatever (people already do that).
This however makes whole game pointless, as we are back where we were.
