I have had a person or two tell me that they have heard turkeys gobble in the middle of the night. However, I think your time would be better served to get some sleep and get up early enough to try your roosting tactics beginning at the first hint of daybreak. I have often heard birds gobble an hour before sunrise. I think spending the same amount of time that you would spend during the middle of the night, and doing so early in the morning, is a much more effective use of your time.