Aragorn and Gandalf went out of their way to capture and interrogate Gollum and learned about his ring and obsession with it too, what happens if they brought Gollum to be questioned by the White Council in Rivendell and Saruman was present and able to learn everything that Gollum knew about the One Ring?

This would be a sad and hilarious lesson for Saruman learning all about the Ring and seeing how it has driven Gollum insane, Saruman might reconsider his own lust for the Precious because he sees how crazy is or he can offer him a job as his servant if he brings the Ring safely to him away from Sauron, his voice would work on a fool like Gollum easily.

Seeing Gollum and Saruman become friends and allies would be dark and terrible too, Saruman would have two pitiful servants Grima and Gollum.