You do not have to have anything to take the written for the ATP. In fact, you can be off the street never having even seen an airplane. You probably won't do that well (unless you used ShepardAir, which I highly recommend).
But, what you do have to have is the Commercial (however you get it, mil equiv or not) in order to take the ATP practical.
Hope that helps. If you are military, PM me for some super gouge on getting through the ATP process.