I think given our common understanding of the word "exists", what you said is possible. 

Though the thing that has no causal effects would be completely unknowable. Think of an invisible, untouchable dragon floating in your room. 

David Lewis talked about such a thing in his discussion of Rae Langton's scholarship on Kant [Ramseyan Humility][1]. He calls them "Idlers", which are 

> those fundamental properties, if any, that are instantiated within the actual world, but play no active role in the workings of
nature. 


  [1]: https://andrewmbailey.com/dkl/Ramseyan_Humility.pdf