As a burner, Forester and Wildlife Biologist, here's my opinion on burning and timing. As a rule, burning the woods is beneficial for turkeys and burning some is better than burning nothing.
Burning keeps the understory in good shape for turkeys to nest, raise broods and move about safely. Areas that are regularly burned typically have good broomstraw understories that are good nesting cover in the years they are not burned, especially 2 or 3 years after the last fire. Areas burned in the spring are good insect production areas, therefore good brood habitat the summer they are burned. The open nature of a burned woodland is also attractive to turkeys because they can see well through the woods and spot predators.
When we have a block, say, of 3 year rough broomstraw with some scattered shrubby cover in a pine stand that the landowner wants burned, we are highly aware that it is good nesting cover and we typically wont burn it between mid April and mid May (peak incubation period). If I burned it in early April, I might burn up a nest that was being laid into but the hen is highly likely to renest. If it is burned in early may after a few weeks of incubation, it is a much more significant loss. She will still probably renest but it will be late and she has wasted valuable and risky incubation time. In areas that potentially hold nests and we are burning in Early April, research has indicated (and our experience show it to be true) that most nests are near an edge, often in the transition with a hardwood drain where the fire will often not burn the nest or go around the thicket. Researchers have found that some nests still hatched after a cool fire went over them but most nests in a burn block were never burned. We have flushed hens from nests occasionally from a nest and in that case we protect it so that fire does not get to it. We have had great success with this and most have hatched. If we hold off because a site is in peak nesting season and great nesting cover, we will burn in later May or June and still get good burn results. The only concern here is flightless poults and we hope that they are 1) not in this thick cover and 2) the fire is moving slow enough to allow the hen to lead the poults to the nearest drain. We don't encounter flightless poults often but I did come up on my partner once running around in the grass bent over and I asked him what he was doing. He said he was catching poults and moving them to the side we weren't burning! The hen was right there.
Size matters but not usually on most private lands. Burn blocks less than 200 acres or so are best and closer to 100 is probably best. Occasionally large landowners and, certainly, public lands will burn large blocks in the hundreds or thousands of acres and there is no doubt this is detrimental to turkeys and other wildlife. Size of burn blocks should be based on animal size and home range. Quail blocks should be 10, 20 acres or so since their home ranges are 100-300 acres. Turkey blocks should be less than 200 acres since their home ranges are 1,000-2,000 acres. Research has also shown that they are reluctant to travel more than 250 yds from the edge into a large burn and use decreases at about 100 yds. With that rule, a 500 acre burn can still be useful if it is less than about 3-400 yds wide but much longer.