Yes, you can play as Batman. More than one of them actually. Lord of the Rings Online developer Turbine are doing the honours on this one and if any of their usual care and love for licenses shines through, it will truly be a thing to behold. It’s coming in the fall to PCs, bringing what sound like destructible map environments and an evolving storyline.
While Nightmare Batman, Gaslight Batman, The Joker, Wonderwoman, Gaslight Catwoman, Gaslight Joker, Green Lantern, Doomsday, Flash, Poison Ivy, Shazam, and Zatana will make an appearance, Superman is missing in action, most likely due to being a gameplay balancing nightmare.
Source Infinite Crisis