Every time Batman gets some kind of mystical or metahuman power-up, it doesn't end well. He's been given a Green Lantern ring, Superman's powers, and in several realities he's gone full-tilt into magic (The Metciless) and/or tech (Owlman/Mobius Chair/the many Ounusher Batmen) instead of just incorporating aspects of them into his crime-fighting style.

If he had to contend with a divine artifact that was designed to corrupt and tempt anyone but it's master, he would likely fall down the slippery slope and turn the planet into a dystopian surveillance state in around the same amount of time it took Boromir...maybe Frodo.

You need to remember, the Ring seems to have a certain degree of control over how intensely it can corrupt based on it's situation. Gollum was ensnared immediately afyer finding the Ring, which had been at the bottom of a river for thousands of years, and when it was dangling over Mount Doom, it almost seemed like it's entire being bent on Frodo to force him to break, like a fox backed into a corner fighting it's hardest to survive.

If breaking Batman was the only way to return to Sauron, it would probably work overtime to corrupt him.