I've had a lot of drunken hypotheticals and thoughts, but can't say that one has ever cropped up. Certainly interesting, without going into the extended thought process of "if Earth had rings, would the Moon do what it does, and if it didn't, would we even be here?"
There's a theory earth had rings at least once in the past, and that the reduced sunlight caused an ice age and mass extinction. It was mentioned in AstronomyCast episode 195.