Turkeys will display whenever they feel like it. My toms display year round,especially when my youngest kid is around them. I think they kind have adopted him as they all follow him everywhere. The drumming usually happens early spring thru early summer. I am not a expert on it but assume this is to bring in hens. To me that drum sound can be felt as well as heard so I am sure travels a great distance.
All the varieties of turkeys can breed with each other. I have Sweetgrass I separate out to get pure Sweetgrass birds. I do release them back into the main flock of mixed breeds,Eastern and Rio Grandes after taking my eggs to the hatchery. That way I get a variety of poults running around here.